Saido Berahino headed an equaliser 10 minutes later and the score remained 1-1 after extra time.
The visitors won the shoot-out thanks to Nacho Monreal's decisive penalty following missed ones from West Brom pair Craig Dawson and substitute Morgan Amalfitano, who had sent a shot against the crossbar in extra time.
The Baggies made eight changes to their starting line-up from their Barclays Premier League win over Sunderland and Keen was encouraged by the team's performance
"I think over the 90 minutes we probably just about shaded it and over the 120 we definitely shaded it," Keen said.
"So to come away without going through to the next round is rather deflating - and the lads are disappointed."