Steve Clarke's men bowed out on penalties at The Hawthorns, and Keen has urged the team to pick themselves up in time for Saturday's Premier League clash with Manchester United.
"I think over the 90 minutes we probably just about shaded it and over the 120 we definitely shaded it," the 46-year-old told the club's official website.
"To come away without going through to the next round is rather deflating – and the lads are disappointed. I think on the night we were the better team. We have to pick ourselves up and get ready for Old Trafford on Saturday.
"You have to give Arsenal a little bit of credit for their resilience throughout, but if you look at the saves Luke [Daniels] had to make there weren't too many. It's really frustrating we can't get a cup run going."
The Midlands club were knocked out in the third round of last year's competition by Liverpool.