With Fulham and Blackburn both winning, Allardyce said he is still feeling the heat with three games to go.
Bolton secured a point thanks to a 71st-minute equaliser from Dean Holdsworth.
It was his first goal in the top flight since August and cancelled out Steffen Iversen's opener.
Allardyce said: "I don't think we are safe yet. With Fulham and Blackburn winning it keeps the pressure on us.
"We have got three difficult games left and we've got to try and get some more points in the bag."
The turning point in the game came when Holdsworth and Michael Ricketts came on for Rod Wallace and Fredi Bobic.
Bolton immediately stepped up the pace to grab what could prove to be a vital point.
There has been speculation about Holdsworth's future but Allardyce said: "I have not had any offers for Dean.
"It was a very valuable goal from him after we had changed our attacking formation.
"That changed the game in our favour after we had fallen asleep and allowed them to score."
Bolton manager Sam Allardyce saw his side hit the 40-point mark with a draw against us on Saturday but insisted: "We are not safe yet."