Matty James drove the Foxes ahead in the 73rd minute but former Newcastle winger Kazenga LuaLua rescued a point for the division's draw specialists two minutes from time with a low shot past Kasper Schmeichel.
Albion missed the chance of opening up a five-point advantage over Leicester but Poyet preferred to concentrate on the positives.
He said: "We definitely deserved to take a point from the game. No doubt. LuaLua's goal could be a very important one for us. We've drawn our last three games and I would say we need to win three of our last five matches.
"It'll be a good number as teams behind us will need to win four. It's in our hands. We can't blame anyone if we don't do it."
Poyet is not too perturbed that Albion have drawn their last three games and stressed: "We're still there. We've plenty of games to play and it's still in our hands.
"We're ahead of the rest and it's up to us to be ahead of Leicester and Bolton. It will only be because of our failings if we don't do it."
Poyet lent his support to Pearson when asked if the Foxes manager could still deliver a play-off spot for the club.
Said the Uruguayan: "Leicester are a very good team. They have power, pace and technical ability and are a very good team to play against. I'm sure Nigel Pearson can turn this run around."