The Seasiders put Brighton under severe pressure after an Ashley Barnes goal put Brighton ahead and Elliot Grandin levelled on 72 minutes - though they failed to find a winner.
Matt Phillips, Alex Baptiste, Tom Ince and Grandin all wasted good chances throughout the contest and Poyet was quick to accept his side were fortunate to earn a draw.
"I am very happy with the result but I don't think it was a fair result because Blackpool were by far the better team so I think we should be delighted with a point," said Poyet.
"Football is a funny game. Sometimes you can create 10 or 20 chances and get nothing. Here we did nothing and I don't know how we scored.
"You can call it luck I suppose and when it happens you are happy to accept it.
"There was no celebration when we scored. The players didn't run and celebrate with the fans, probably because they were so shocked and so surprised to have got a goal at that stage of the game.
"But I won't complain with a point, I will gladly take it.
"But I also knew we would have to defend a lot and we did that well for a while but I think one point is quite unfair on Blackpool already so I won't say we are disappointed not to get all three because we didn't deserve to."
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