"We played some wonderful football at times and created some fantastic chances but we just couldn't get that second goal," Allardyce said after Tuesday nights game at The Reebok.
"After Stelios had been so brave to score the first, Gary Speed and Diouf both had great chances to put the ball in the net early in the second half but failed to do so and I think that was the turning point in the game.
"Now we have to rely on Everton slipping up if we're to get that fourth place."