Robert Tesche scored netted the only goal of the game after 43 minutes to give Blues a deserved 1-0 win at the Macron Stadium.
"The players have got to be given great credit for the way they moved the ball and looked a very controlled team," Rowett said after the game.
"The game suited us because Bolton tried to play through us because they have good technical players in the middle of the park.
"It was about blocking up that area, breaking wide and counter attacking.
"With a bit more composure and better timing in the final third we could have scored one or two more with our breakaways.
"I thought we showed excellent desire to keep going and attack.
"This team has been mid table for two months now but I never once questioned desire to ever go on and win the game.
"We also had just under 4000 of our fans here and as a player you can't help but be inspired by that and feel responsible to go and put in a performance."