Manager Jurgen Klopp complained a dry Anfield pitch made things difficult for their playing style, but Milner was in no doubt where the blame lay and, as senior professional, shouldered the burden.
The 31-year-old’s effort was his first unsuccessful penalty in 13 attempts for the Reds - and his first miss from the spot since November 2009 - and came when Fraser Forster dived low to his right having engaged in some gamesmanship trying to rough up the penalty spot and put off the taker.
“It was my fault for us not getting the three points today, definitely my fault. I take responsibility,” Milner said.
“I’ve been around long enough not to let that (Forster’s antics) worry me. I did what I wanted to do - obviously it was not good enough on this occasion.
“Fraser’s a good keeper. I can’t do any more than hold my hands up and apologise to the boys.
“With these games we knew what we had to do and we haven’t done it. But you can’t create more chances than have a penalty - ultimately that was the big chance and it wasn’t taken.”
The draw moved Liverpool back into third, a point ahead of Manchester City, having played a game more than Pep Guardiola’s men.
It also briefly meant a top-four finish was not in their hands, but Manchester United’s 2-0 defeat at Arsenal later in the afternoon put Klopp’s side back in control of their own destiny.
The Reds have now dropped four points in their last two home matches, though, to set up a tense finish to the season.
“It is not nice to drop points at home but now we play away (at West Ham) and then we have another home game (against Middlesbrough),” Klopp said. “It is only a mental issue if you see it as one.”
Klopp was unhappy with the way Forster and some of his team-mates behaved in the moments prior to Milner’s penalty, awarded after a handball by Jack Stephens in the 66th minute.
“I really don’t like it to make a story of it. You saw what they did,” the German said. “On one side you say it is very smart because he missed and on the other not sportsmanship.
“But whatever I say, we look like bad losers.”
Klopp was not happy with the way the Anfield surface, due to be relaid this summer, played in the May sunshine.
“Today the pitch was really dry. We gave all the water we had and after 15 minutes it was really dry. It was difficult and with a lot of passes you could say, ‘Why are they playing this?’.
“In a home game you have to have the best circumstances but we couldn’t have this.”
Southampton boss Claude Puel claimed the penalty should not have been awarded, and suggested Liverpool goalkeeper Simon Mignolet was perhaps lucky not to have been red-carded for a handball outside his area missed by referee Bobby Madley.
“I think this penalty is harsh,” Puel said.
“Jack turns and the ball falls on his arm, but it was not intentional. The save was important, for Fraser of course, but for all the squad.
“On the other side, there could have been a sending-off of Mignolet when he touched the ball outside his box.”
Puel praised his side for keeping a fourth clean sheet against Liverpool this season, having stood firm in the goalless Premier League encounter at St Mary’s in November and the two-legged EFL Cup semi-final in January.
“Two draws, two wins and four clean sheets is a fantastic job against this team,” the Frenchman added.
“It was difficult for us to make some counter-attacks, but it is fantastic work from the squad.
“We defended very well, with good structure, organisation and discipline.”
Mignolet, Clyne, Matip, Lovren, Milner, Can, Lucas (Lallana 69), Wijnaldum (Grujic 87), Firmino, Origi (Sturridge 69), Coutinho.
Karius, Klavan, Moreno, Alexander-Arnold.
Forster, Cedric, Stephens, Yoshida, Bertrand, Tadic, Davis, Romeu, Ward-Prowse, Boufal (Redmond 60), Gabbiadini (Long 69).
Rodriguez, Caceres, Hojbjerg, Pied, Hassen.