City created chance after chance but were denied by the goalkeeper, last-ditch defending, or the woodwork in a bid to level Che Adams’ 16th-minute goal.
The Catalan said his players couldn’t have done much more, but admits there must be fewer losses next season.
“We played well and with honesty, character, and desire to try until the end,” said Pep.
“With 10 Southampton players on the penalty spot, it's difficult.
“I am so proud. I like the way we played but it's not enough. It's not a complaint of the players. Far from it.
“The game was a little bit of a repeat of how some games have gone this season - one mistake and they punished us.
“After, we created a lot, but as I say, they had 10 players behind the ball.
“We conceded few chances and played a really good performance, but it was not enough and we have lost a lot of games this season - and we cannot compete for the title doing this.”
Asked whether Ederson being so far off his line when Oleks Zinchenko lost possession had been targeted by Southampton Pep said it was just a mistake that was clinically punished.
“We use our keeper to start our build up to play - to play better; he gives us a lot. The mistake is part of the game,” he said.
“We didn't lose because of this reason. It’s happened many times - these kind of situations and the amount of chances we had - it’s football. We tried so hard.
“In general, mentally, the games we played are more than good.
“We lost today but we cannot say we are not a team who doesn’t score goals this season. We are leading in goals scored and created so many chances.
“Of course we have confidence in the players and we are the same guys.
“We've done it in previous seasons. The way we played is similar, but we have to win the games.
“Next season will be next season. We will try to score more goals and avoid conceding chances.
“The control is there, the way we play is there – we need to try to increase these kind of things.
“The Liverpool result is in the past; Southampton is also now in the past.”