Sam Vokes and Danny Ings ensured Dyche made a winning return to his former club and lifted his current side to within four points of the play-offs.
"It is good fun climbing the table," Dyche said after a third win in a row. "I wish it was easy enough week in, week out. You've got 11 each week out to get you but the feelgood factor is there.
"I want us to win as many games as possible and who knows where that can take us? That's the challenge, quite simply.
"We're in the hunt right now but we can only take it one game at a time. It was a very good performance against Millwall and a very good win for many different reasons.
"In the first half we were on top but in the second half they made it tough. We didn't start well, the first seven or eight minutes of the second half is the only part I'm not happy with.
"We controlled the feel and tempo of the game in the first half. In the second half you expect a reaction from any team, especially Millwall, so it was tougher but we held on."