The Saints matched their visitors in a tight first half, but second-half strikes from Vincent Kompany, Leroy Sane and Sergio Aguero took the game beyond the home side as City ultimately cruised to all three points.
Puel had no complaints with the final score, claiming that nerves in possession may have been a reason behind his side's below-par performance.
"In the second half they scored two goals on the counter-attack, but I thought we could have done better today. We simply did not play well enough against this team, nervous with the ball," he told BBC Sport.
"It's a disappointment because we can do better, we can create better opportunities. We did not have enough today, we were not sufficient. It was not a good day for us, but congratulations to Manchester City.
"Today, we have them too many opportunities. Against good teams we have to show our best qualities, to defend well and show better organisation."
The defeat leaves Southampton ninth in the Premier League table.