Saints went in front early in the second half at the Etihad Stadium when Rickie Lambert and Steve Davis both found the net soon after coming off the bench.
However, goals from Edin Dzeko and Samir Nasri meant the champions ran out winners.
Saints boss Adkins sprung a surprise by leaving Lambert out of his starting line-up at the Etihad after scoring 27 goals in the Championship last term.
However, he felt it was a better use of Lambert's abilities to have him fresh for the latter stages.
"I would have thought he was upset because everyone wants to play," he said.
"But I have to make decisions.
"We came up with a game plan and he was on the pitch to score when it mattered.
"We expected the opposition to have a fair bit of the ball, so instead of Rickie running round and being shattered, he was on the pitch, scoring a goal and being a threat."
Adkins also confirmed he expected more signings before the August 31 deadline, although offered no update on the deal to get Ramirez to the club, amid reports the transfer is close to collapse.
"We have been linked with a few players," he said.
"I don't know if there are any more developments but there will be more players coming into the club before the transfer window shuts."
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