The Cherries had more attempts on goal than their Premier League opponents in Saturday's fourth-round tie at Dean Court, but went down to efforts in either half from Victor Moses and Daniel Sturridge.
The Reds scored both of their goals during periods of sustained Bournemouth pressure.
"I don't think it [a positive result] was far away," said Cherries boss Howe afterwards.
"Everyone says goals change games and they do because with their first real attack they have scored and showed the cutting edge that we didn't unfortunately."
Liverpool were knocked out away to Oldham at the same stage last season, when the Latics employed a much more physical approach than Bournemouth's.
However, Howe insists he will always try and play football, whoever the opposition may be - a philosophy which was praised by Brendan Rodgers.
"Our players are not built that way and we don't recruit that way," he said when asked if a more physical game would have offered more of a challenge to Liverpool.
"We are trying to build a club that is club here that is built of possession very much like Liverpool, we very much want to go down that route.
"This was a chance for us today to go toe-to-toe with a really good football team and see if we could beat them footballing-wise.
"On another day with better decision making in and around the box, we could have led at half-time."