Howe made 11 changes to his side who were 2-1 winners over the Championship outfit at St. Andrew’s in the FA Cup Third Round.
Glenn Murray struck late to seal their place in the Fourth Round and Howe admitted he was pleased to avoid a replay, with next week's Premier League games against West Ham United and Norwich City already having a bearing on his team selection.
"First things first we're very pleased to get through," Howe said.
"No doubt it was going to be a very tough game as Gary Rowett has his side well organised and difficult to beat.
"The selection was down to us having a Premier League game in two days time, so we wanted to protect the majority of our squad if we could while still playing a team to win the game.
"It's a delicate balance, by no means did we pick a team to do anything other than to try and win.
"It was wise to make the changes we did."
Youngsters Matt Butcher and Jordan Lee made their first starts for the Cherries in the line-up and Howe was full of praise for the academy players who stepped up in each full-back position.
"The team did well and the youngsters did very well,” he continued.
"It was difficult for Matt Butcher as he's naturally a centre-midfield player so he played out of position, but he did well.
"Jordan Lee was another good performance. He's been thrust into action and hasn't had a lot of training time with us.
"We believe in the players and they did well in a development game last week and stepped up to do excellently again."
Supporters can now watch a full post-match interview with Howe, as well as his pre-match press conference, on Cherries Player HD.