Victory would have given Albion a five-point cushion on their seventh-placed visitors, but in the end it took a Kazenga LuaLua goal two minutes from time to secure a 1-1 draw.
Bolton and Leicester are just two points behind with five games to play, but a positive Poyet said: "It's in our hands.
"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. We can't blame anyone if we don't do it.
"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."
The point for Leicester was just their third in eight games, but Poyet said: "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."