The Premier League side went into the game off the back of a 4-0 thrashing to Burnley at the weekend, with Callum Wilson's late header securing progression for the 'Cherries' after their Championship opponents had come back from two goals down to level.
Howe made nine changes to his starting XI for the game and admitted post-match that the win was the perfect way for his side to get over their loss to the 'Clarets'.
"We desperately needed a performance tonight after the Burnley game, of course we needed a reaction," he admitted. "You feel better but still Burnley is not far away in my thoughts. That's just how I am and until we put that right in the Premier League that will still be with me
"I'd say (tonight) 90 per cent was positive. I thought we played some good football and then suddenly bang, bang, we concede two goals.
"Only we could do that to ourselves. We shot ourselves in the foot twice, made some bad decisions and then it's in the balance.
"And then you're thinking the lottery of a penalty shoot-out was going to be the outcome of the game and it should never have been in that position.
"But credit the players again because we get ourselves in these positions and sometimes we get out of that hole we're in because of our attitude, because of our spirit."
Blackburn boss Tony Mowbraw wasn't overly fussed with exiting the competition, though he admitted his frustation with the referee's decision to award Bournemouth a penalty after Darragh Lenihan was adjudged to have fouled Jordon Ibe.
"I'm not sitting here overly concerned about the Carabao Cup," Mowbray admitted.
"We left our front five all at home tonight ready for the weekend, ultimately it’s disappointing because you want to try and win football matches and I thought we competed pretty well.
"Ultimately, it might be a blessing in disguise to get out of this competition so we don’t have to do five-and-a-half-hour trips down to the south coast so we can concentrate on our league games."
"I thought their penalty was a shocking decision but there you go, we move on, let’s get on the bus, let's get home and get ready for Saturday," he added.
"I've watched it five times, it's never a penalty in a million years but he's given it, it's in the history books, we have to get on with it."