The former England worldwide saw his second-half spot-kick saved by Saints goalkeeper Fraser Forster and the result now leaves Liverpool's Champions League hopes hanging in the balance.
Jurgen Klopp said Liverpool deserved to beat Southampton but was unhappy with the Saints' defensive tactics in the 0-0 draw at Anfield.
Klopp said: "Look I really don't like, even after we've only drawn, to make now a story of it". "We gave all the water we had and after 15 minutes it was really dry, the wind and a little bit..."
"As everyone could see, it was a hard game, Southampton played in a specific way".
"In a home game you have to have the best circumstances but we couldn't have this".
The result left Liverpool in third place in the Premier League table and on 70 points with two games left to play this term.
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But Klopp's side never got started against a Southampton team who had Fraser Forster to thank for a string of outstanding saves.
Forster gathered a Georginio Wijnaldum header and Roberto Firmino had a shot blocked by Maya Yoshida as the Liverpool attack probed at a deep-lying Southampton defence during the opening stages.
"We have only one point more, we wanted to have three points more". Milner cuts back onto his right foot and whips in a cross which Grujic flicks goalwards but Forster is there to tip over the bar. Klopp's side have taken only two points from their last three games at Anfield, in contrast to three consecutive wins on the road, with their recent home form stalling the pursuit of Champions League qualification. This means little when you consider the former has played a game more and has an inferior goal difference after the City thumped Crystal Palace 5-0 on Saturday.
Second-half goals by Billy Jones and Jermain Defoe earned bottom club Sunderland a first win in 11 games and condemned Hull to a first home defeat under Marco Silva.
The missed penalty followed a handball from Jack Stephens and Milner's effort may have been affected by words uttered by England colleague Forster, but despite the miss, Puel was disappointed with the decision.
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.
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