Sir Alex Ferguson's side have seen their seven-point lead reduced to one with a match in hand in the last fortnight.
United still have to play Sunderland, Portsmouth, Middlesbrough and Hull - all teams Megson considers relegation rivals to his team.
The ginger gaffer had previously expressed concerns that had United run away with the title, they may have turned their attentions to the Champions League and eased up on the domestic front.
But with things so close at the top of the table, Megson is confident United will not be able to take it easy.
"The situation right now is so tight that there isn't anyone not playing for anything," he said. "No-one can honestly say they are not playing for a place in Europe, or to avoid trouble, or going for the title.
"I don't want to be rude to Manchester United but they have got to keep playing now.
"With what happened on Saturday (losing at Fulham), they know that every team they play they will have to go and get a result.
"We've played them twice and they've turned us over twice - maybe rightly so - but they have got to keep going now right to the end."
Bolton are currently 12th in the table on 34 points, five above the relegation zone, but Megson said they were not yet safe.
"We know that there is a huge game on the horizon with Middlesbrough (on Saturday week)," he told the Bolton News.
"If we can beat them, then we will do ourselves a huge amount of good."
Prem Relegation 2008/09 Win Outright: Bolton 10/1