The Cherries were beaten 2-0 but were unlucky not to be ahead when Charlie Daniels had his penalty saved by Joel Robles in the first-half.
Matt Ritchie and Junior Stanislas also went close in the second-half and Distin believes that the Cherries suffered from a bit of misfortune as they were eliminated in the fifth round.
"The result is obviously disappointing but it was a good performance," the 38-year-old said.
"We didn't have much of the possession but we were still dangerous. We had a bit of bad luck, the first goal was a deflection and apart from the second goal they were not that dangerous.
"We're not used to not having a lot of the ball so that was a good test, I think it was a good team performance and individually everyone was up for it.
"It's a very strange feeling as you feel as though you've done enough but you've lost 2-0 and are out - despite that there are a lot of positive things to take from this stage."
The French defender doesn't believe that the exit from the cup will affect the remainder of the Cherries'campaign, and believes the spirit in the dressing room will stand them in good stead for the run in.
"The work rate is really high at the club," Distin continued.
"We have a good team spirit in the dressing room and everything is there to have a successful season.
"I don't think the cup was a distraction and it won't be easier in the league now we are out. We change the squad in the cup so we saw it as a good opportunity not a distraction.
"We have an important run in now and there are some big games for us. We're disappointed to be out but we have to look ahead."
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