Brett Pitman scored in the 31st minute to give the visitors all three points at the Keepmoat Stadium.
After the match, the manager told BBC Radio Solent: "It was an important win for us because you don't want to go into a two week break on a downer. The only disappointing thing for us was that it was only 1-0 because we had numerous chances.
"You do feel that if you don't take those chances, then only one lapse in concentration or one long ball into the box and they could score. But I thought the two centre halves and the back four were excellent, the lads worked their socks off and we got the win we needed.
"Games in the Championship are difficult to win and it's incredibly difficult to keep clean sheets against good strikers. To do it here is a good achievement, especially with what happened last year and the battle between the two clubs. It was nice to come out on top today."
Bournemouth sit sixth in the Championship table.