Mark Davies scored the only goal in the 41st minute when he ran on to namesake Kevin's through-ball to fire past goalkeeper Luke Daniels.
Megson, however, was still jeered by the travelling fans who have never taken to the former West Brom boss, who presided over two successive defeats before tonight.
"It was a high-pressure game for us because of what has gone on in the two Premier League games so far," he said.
"There was a huge amount of pressure on the players tonight and that is why we put out the team we did.
"We needed to get a victory and needed to get through and we have managed to do that.
"We haven't played anywhere near as well as we did at Hull at the weekend but we have kept a clean sheet and I thought we could have scored even more."
Megson brushed aside criticism of his side from many quarters after two successive league defeats.
"For some reason Bolton seems to be viewed entirely differently from the 19 other clubs in the Premier League. We need to change that," he added.
"I was watching television today we were described as Bolton, who haven't won a game all season - it didn't say the season was nine days old.
"It motivates me and it motivates the players. We have to keep everything within the four walls of the dressing room.
"There is not a great deal of assistance from anywhere else but we get on with it.
"Today the fans were chanting 'Megson give us a wave'. I turn around and wave and get booed! To be perfectly honest that's normal.
"The players in the circumstances have been fantastic because it is a lot harder for us than most."
After a 3-0 drubbing at Leeds at the weekend Tranmere manager John Barnes was pleased with the display of his team.
"I was pleased with the performance, the attitude, the commitment and the desire," he said.
"We can all have bad days but the attitude and desire against Leeds was unacceptable, whereas tonight they really did put in a shift against a strong Bolton side."