The Trotters are currently 11th in the Premier League table but the bottom half is so congested they are just five points clear of the drop zone.
Megson admits he was disappointed with the attitude of his men in the 2-0 defeat to Stoke last week and he wants to see a positive response against Fulham on Saturday.
"A team that is absolutely desperate to win a game of football will always overcome one that isn't," he told the Bolton News.
"We've got to get ourselves into that desperate mindset against Fulham.
"We need to really start competing because in the last game, Stoke looked like they wanted it more. They were prepared to do that little bit extra.
"Although it might stick in the throat a bit, it was complacency. We had won our last two games, we were in that mid-table bit where we still are and we wanted to push on from there.
"It was disappointing but hopefully now a lesson has been learned and we can crack on again."
IntensityMegson has also challenged Bolton's supporters to play their part over the final two months of the season.
"You look at the atmosphere and intensity at the Britannia, from the supporters and players, it was incredible," he said.
"Then at the other end of the scale, Liverpool against Real Madrid the other day - it just absolutely blew them away in the first half.
"That has got to be your starting point. You may not be able to pass the ball as well as Liverpool's players, or finish as well as Liverpool's players, but everyone can show that same desire, drive and intensity to get after games properly.
"It applies to the supporters too because they can be a real help."