Allardyce was without the likes of Andy Carroll, James Collins and Winston Reid for the defeat at The Hawthorns, as a Browne Ideye double and goals from James Morrison and Saido Berahino ensured Albion's progress to the quarter-finals.
With substitute Morgan Amalfitano sent off late on, Allardyce had no complaints about a dismal outing and refused to criticise his players.
"I wouldn't say I was shocked by it, it's probably been coming based on what we've had to cope with over the last few weeks," he told BT Sport.
"I think it told on us today, there's no doubt about that. I have to give West Brom a lot of credit too - they were very good.
"I look at the players and there was not the energy we know they've got based on what they've been through in the last few weeks - especially this week.
"We played a huge effort on Sunday against Man United and then we had to do 30 minutes with nine men against Southampton on Wednesday.
"Those two games have really caught up with us today. Those players couldn't get near the energy levels we know they can and we couldn't live with West Brom in the end.
"I'm not going to criticise my players, they've given everything they've got. Anyone who says they haven't doesn't know much about football."
On the Amalfitano dismissal, which saw two yellow cards issued in quick succession for a foul and subsequent push on Chris Brunt, Allardyce said the decision mattered little in the context of the game.
"It's unprofessional isn't it? The punishment is laid down in our code of conduct and by the Football League," he added.
"That will be dealt with internally and we move on. I don't think it would have made much of a difference to the result, I don't think we'd have got back into the game."
