Manuel Pellegrini's men could not build on their impressive 3-2 midweek triumph over West Brom at the Hawthorns and have now won only two of eight Premier League away games this season.
Sergio Aguero's 18th goal of the season gave City an early advantage, but it was left to rue a moment of rare profligacy from the in-form striker when he missed an excellent chance with half an hour played, before Dani Osvaldo struck a magnificent 42nd-minute equalizer for Southampton.
Milner paid tribute to an impressive performance from the injury-plagued hosts, who ensured that City's record on its travels remains in stark contrast to seven wins from as many Premier League outings at the Etihad Stadium this season.
"They probably had most of the play in the first half but we had some pretty good chances and if we'd have put them away it might have been a different game," the England midfielder told City’s official website. "But that seems to have been the season for us away from home - the chances haven't quite gone in and things like that and that's the difference [with the home form].
"They [Southampton] are a very good team, we know that. They've got a lot of very good young players and they're an exciting team to watch. It was a good game, but we didn't perform and play our part in what would have been an even better game if we'd played to our potential."
Milner believes that a point was still an acceptable result when compared to earlier City losses this season – such as those in games they controlled for long periods against Aston Villa and Sunderland.
"You can think of at least three of the games we've lost where we've played really well, dominated the game and come away with nothing," he added. "We weren't quite at our best and they probably had the better of the game but we've come away with a point.
"It's disappointing. These are the games we want to be winning but it's better than coming away with nothing."