Blues, who had captain Paul Robinson sent off late on, had looked to be heading for a surprise win when Clayton Donaldson and David Cotterill struck in three first-half minutes but strikes from Steve Cook and Callum Wilson saw the hosts go into the half time break on level terms.
A Yann Kermorgant penalty right at the beginning of the second half gave the Cherries the lead and they completed a 4-2 win with a Charlie Daniels strike 16 minutes from time.
"For 35 minutes it was our best attacking display of the season but we didn't quite have the mentality to see it out," Rowett said after the game at The Goldsands Stadium.
"We caused one of the the best attacking teams in the league at home a whole world of problems.
"We have to be a little stronger in terms of our mentality and see the half out.
"You cannot work that hard to get into a winning position and come in at half time 2-2.
"That's the two sides to our team at the moment, we need to see those games out."
"Bournemouth are a fantastic side. They were under pressure at 2-0 but they showed great patience and were rewarded for that in the end."