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Chelsea winger Sinclair, who arrived on loan in the week after an unhappy stint at Charlton, was also booked for diving in the second of the shouts much to the dismay of Warnock.
Blackpool could have taken a 19th minute lead when Gary Taylor-Fletcher was played clean through, but was denied by an excellent save from Julian Speroni.
Sinclair then had the home fans on the edge of their seats with an angled lob which landed on the roof of the net two minutes later.
The visitors responded and first Ian Evatt headed a corner marginally over the crossbar, before Claus Jorgensen drilled a low shot into the side-netting with team-mates waiting for a cross.
Stephen McPhee then drew a save from Speroni with the Argentinian keeper able to recover from fumbling the effort to gather the loose ball ahead of the advancing Ben Burgess.
Palace improved after the interval with a renewed vigour, largely due to the booking of Sinclair during the non-award of a penalty just before the interval.
Half-time substitute Reid looked lively and produced some dangerous crosses from the left flank.
The West Ham youngster also tested Paul Rachubka with a low shot on the hour mark, but the effort was easily held by the Seasiders keeper.
Palace upped the pressure in the final ten minutes and were virtually camped in the Blackpool half, as they went in search of the points.
But they were almost hit on the break in the 89th minute when Wes Hoolahan capitalised on a slip from Mark Hudson, but took his time when one-on-one with Speroni and the keeper saved the day.
At the other end, Reid's right-wing cross teed up Ashley Robinson, but his downward header lacked the necessary power to break the deadlock.