Palace were left frustrated despite all of their new signings making promising debuts.
Scott Sinclair was the pick of the bunch, showing skill and penetration in abundance, but he could not inspire the Eagles to what would have been a crucial victory.
Palace manager Warnock wasted no time in thrusting his newly-installed recruits into action.
Fulham loanee Nathan Ashton came in at left back for the injured Clint Hill while Chelsea left winger Sinclair replaced Sean Scannell, who was relegated to the substitutes' bench.
Fit again Danny Butterfield came in at right back, meaning Jose Fonte took up a place in the dug-out.
They were the three changes from the starting line-up that came away with a 2-2 draw at Sheffield Wednesday a week earlier.
This week's other new signing, West Ham midfielder Kyel Reid, began from the bench. Blackpool, meanwhile, fielded an unchanged side to the team that came away from promotion-chasing Stoke with a point last Saturday, apart from adding ex-Palace forward Paul Dickov to the substitutes' bench.
A dull start was sparked into action on 13 minutes when Ashton went on a run down the left wing. He appeared to be upended in the penalty area by Ian Evatt but, despite loud calls for a spot kick, referee Alan Taylor allowed play to continue.
Ashton's attack-minded approach earmarked him as Palace's brightest early performer in a promising start for the home side, but Blackpool soon got into the game and could have taken a 19th-minute lead were it not for Julian Speroni's save from a clean through Gary Taylor-Fletcher.
Sinclair, making his debut alongside Ashton, showed what he could do two minutes later with an angled chip that landed on top of the net.
But it was Blackpool who looked the more dangerous. A right wing corner caused panic in the home area. Matt Lawrence's clearance fell for Evatt, but his header ended up marginally over the bar.
Claus Bech Jorgensen then wasted a promising opening for Blackpool on the half-hour mark. With Stephen Crainey unmarked in the middle, he decided to go for goal from an acute angle and could only find the side-netting.
Four minutes later, Blackpool again caused fear in the Eagles rearguard. Steve McPhee, left unmarked in the box, struck at goal and Speroni saved. But, in soggy conditions, the Argentinian failed to hold the ball and it spun behind him and almost presented Ben Burgess with an open goal rebound. But Speroni recovered in the nick of time to gather the ball and avert a goal.
The opening half's most controversial incident came seven minutes before the interval. Clever play by Clinton Morrison paved the way for Sinclair to find space in the area. The winger appeared to be clearly brought down by Kasper Gorkss but, instead of pointing to the spot, Mr Taylor pointed the finger at Sinclair and booked him for diving.
The decision infuriated both home fans and players, and led to a minor scuffle and subsequent yellow cards for Palace's Tom Soares and Blackpool's Evatt.
The sense of injustice seemed to reignite Palace. Watson's long distance strike swerved wide before Sinclair delightfully dropped his shoulder to eliminate a defender and drove over the bar with his left foot.
In the 45th-minute, the visitors produced a move of real quality. A deep cross from the right was perfect for Burgess to head in the direction of a forward-running Jorgensen. But again, his shot missed the target.
On the stroke of half time, James Scowcroft picked up an injury that required sideline treatment during the interval.
The targetman failed to emerge after the break, enabling Reid to make his debut, and Warnock also replaced Ashton with Fonte at the interval.
Reid showed his potential by finishing off a lengthy passing move with a 53rd-minute cross that was cleared from the danger area.
Palace looked lively going forward but Derry was forced into making a drastic tackle on the counter-attacking McPhee which earned the midfielder a booking on the hour.
The Eagles were beginning to pose more of a sustained threat, especially down the left, where Sinclair and Reid combined to good effect on 67 minutes. The latter's low cross, however, was cleared.
Reid had made another run four minutes later but his shot did not trouble away stopper Paul Rachubka.
With 16 minutes remaining, Ashley-Paul Robinson came on for Tom Soares to provide more attacking options.
On 80 minutes it was Blackpool who had a penalty shout. Wes Hoolahan capitalised on a sloppy pass by Danny Butterfield and fell under a challenge from the same player. However, Mr Taylor again played on.
Shortly afterwards Dickov, who had ben playing in recent weeks due to a hamstring injury, replaced Gary Taylor-Fletcher for Blackpool.
As the game drew to its conclusion, Palace camped the visitors in their own half. Their pressure was obvious, but chances were less clear cut. Robinson's weak shot, following Ben Watson's dangerous corner, was a case in point.
With one minute of normal time remaining, Mark Hudson's slip let in Hoolahan. With the goal seemingly at his mercy, Hoolahan took his time and was odds on to score. But Speroni yet again rescued Palace with a diving save.
Three minutes of injury time gave Palace further opportunities to break teh elusive deadlock and Sinclair's blocked shot fell invitingly for Reid, but his shot was cleared.
As it reached a thrilling finale, the game swung from end-to-end. Substitute Grant Holt's near post shot flicked over the bar before, with seconds remaining, Reid's right wing cross set up Robinson but his downward header lacked power.
Attendance: 16,028 (Away 976).
Palace: Speroni; Butterfield, Ashton (Fonte 46), Lawrence, Hudson (c); Soares (Robinson 74), Derry, Watson, Sinclair; Scowcroft (Reid 46), Morrison.
Subs: Fletcher, Scannell.
Booked: Sinclair (38), Soares (40), Derry (60), Butterfield (78).
Blackpool: Rachubka, Crainey, Evatt, McPhee (Coid 90 +3), Woolahan, Taylor-Fletcher (Dickov 81), Jorgensen, Gorkss, Barker (c), Burgess (Holt 81), Flynn.
Subs: Morrell, Fox.
Booked: Evatt (40)
Referee: Mr A Taylor. Assistant Referees: Mr S. Beck, J. Magill. Fourth Official: D. Margetts.
