Despite taking a half-time lead through Jo, City were undone by two goals in as many second-half minutes on Wednesday night.
Mancini ended the contest with £100million worth of talent on the pitch, but it was not enough as Boaz Myhill turned away James Milner's last chance at a rescue mission.
The City boss might reflect on his decision to select six youngsters in his starting line-up.
However, with Chelsea due at Eastlands on Saturday lunchtime, Mancini claimed he had no choice.
"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 12.45pm, the time to recover is very short.
"They would need minimum three days so to play tonight would have been dangerous."
There is a school of thought that feels Mancini would have been better served in the long run naming his strongest side this evening, then assessing what he had left for Chelsea.
Unless he is intent on winning the Premier League title - and the Blues are already seven points adrift of Chelsea - the Carling Cup was the easiest way of ending the club's 36-year trophy drought and offer some tangible reward for Sheikh Mansour's £1billion investment in the Eastlands outfit.
Mancini took an alternative view.
"Saturday is more important, the FA Cup is more important. The Europa League is more important," he said. "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?"
West Brom assistant boss Michael Appleton understandably declared himself delighted with the outcome, rejoicing at Simon Cox's winner that followed a Gianni Zuiverloon leveller City were convinced should have been a foul on Ben Mee.
"It was a great result. Really positive. We made numerous changes and the lads responded well," said Appleton.
"We were second guessing their side bearing in mind they have Chelsea on Saturday but there was still a lot of experience in the side.
"They brought the cavalry on at the end and we were under the cosh for the last 15 minutes but we did enough to win."
The only plus point for City was the performance of Shay Given, who declared on Sunday his belief that it did not matter how he performed, he would never get selected above new Blues number one Joe Hart.
It seems certain Given will leave the club in January, although he could not have done much more this evening given he stood between City and a very embarrassing defeat.
"Shay Given played very well," said Mancini. "I am very happy for him.
"He deserved a night like this. He is still a very good keeper."