Millwall have gone 17 games unbeaten in the league since losing 2-1 to Norwich City on New Year's Day, and Kavanagh admits that he can barely believe how well the Lions are doing.
"We're enjoying ourselves. The first target was to stay up, we achieved that and then we said 'let's see where we go to'," Kavanagh told Sky Sports News.
"It's game by game. Friday night, it is a fantastic game. If you said to me at the start of the season that this is what would be going on, I would have pinched myself. I wouldn't have believed you.
"We're there now, there is not a lot of pressure on us. We're just going to enjoy the night and then it's onto the next one. Let's see what happens."
Millwall were last in the top flight in the 1989-90 season.