A first-half strike from Mauro Boselli was enough to settle the close-fought tie in Wigan's favour.
It is the first time Howe has tasted defeat since he returned as Cherries boss, a run of 18 matches, but the former Burnley manager was pleased with the effort from his side.
"I thought it was a really good game and Wigan showed us a lot of respect with the team they picked," he said. "It was a strong team and we were slightly disappointed with our first-half performance.
"I think in the second half that all changed and we had a right go at Wigan and threw everything at them and, apart from their goalkeeper making some good saves and the woodwork, I think we would have deservedly forced extra time.
"I think it was a really good effort from the players, we did not necessarily lose it and I think Wigan won it. If a team was going to beat us, they were going to have to earn it."
Boselli's goal came courtesy of a mistake from Bournemouth midfielder Harry Arter, who lost possession to the Argentina striker before he fired Wigan ahead.
And Howe acknowledged that, against top-flight opponents, such errors do not go unpunished, as he said: "That is the difference between the levels really.
"On another day we would have got away with that mistake but we didn't and we got punished."
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