The Italian tactician fielded an under strength line-up for the third round clash at The Hawthorns but his plan backfired when the Baggies came from a goal down to score twice shortly after half-time.
Mancini insists he had no choice but to change his squad around ahead of the vital clash with league leaders Chelsea on Saturday.
"I don't regret making the changes," he said.
"I have big problems at the moment and we couldn't take any risks. If I had more players available it would be a different team.
"But when you play like us and Chelsea, on Saturday at 12.45, the time to recover is very short.
"They would need minimum three days so to play tonight would have been dangerous."
Mancini admitted that the other competitions City is in are more important than the Carling Cup although he did admit it was a great chance for some of the younger players to get a start.
"Saturday is more important, the FA Cup is more important. The Europa League is more important," he added.
"I did not regard this as a necessary sacrifice. We wanted to win. That is why I had four senior players on the bench.
"But I knew there was a chance we could lose because we started with six young players.
"I am happy with these guys. We might have lost the game but they can improve. If they do not play tonight, when will they ever play?"