Brett Pitman's first-half opener counted for little as Lee Hughes and Craig Westcarr struck after the break to send big-spending Notts County into today's third-round draw.
Once Cherries had fallen behind, their hopes of forcing their way back into the game were not helped by heavy rain which made the Dean Court surface extremely difficult to play on.
Giving his verdict on the match, Howe said: In the first half I thought we were excellent. Without really creating too many chances, I thought we controlled the game.
We started the second half, conceded two poor goals from our point of view and, of course, the heavens opened and the last half an hour was a write-off.
It was a lottery at the end. In the last half an hour you couldn't run with the ball or do anything with it.
I don't think there was a lot wrong with how we played but they were just really disappointing goals from our point of view. To win games, you can't give teams goals.
Cherries' hopes were dealt a severe blow prior to the clash when goalkeeper Shwan Jalal was ruled out by an ankle injury sustained in training on Thursday.
Rookie Dan Thomas got the nod and Howe felt the 18-year-old did well.
I'm sure he enjoyed the game, said the Cherries boss.
It was great for him to make his home debut and the crowd really supported him.
It's a great opportunity for Dan and he's got to grasp it not just in games but in training every day.
He's probably had this earlier than he'd have thought but it's up to him to prove he's good enough.
Howe added: Everyone knows how much we wanted to get through, not only for the financial rewards although that was a big incentive for us. Everybody at the club would have loved to have seen us get a good third-round draw.
It was more for the players who wanted to continue the good run we've been on and get in the hat because it's a great competition.