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The key moment of a largely drab game came in the 65th minute when Saints goalkeeper Fraser Forster denied Milner from the spot.
A frantic finish did not return a winner for either side, and Liverpool now again need other results to go their way in the run-in if they are to qualify for next season’s UEFA Champions League.
Squawka News provided both starting lineups ahead of kick-off:
Squawka News @SquawkaNews
Southampton XI vs. Liverpool; Forster; Cedric, Yoshida, Stephens, Bertrand; Davis, Ward-Prowse, Romeu; Tadic, Gabbiadini, Boufal.
A subdued Anfield was treated to a dire first half, the first shot on target coming from Philippe Coutinho in the 24th minute.
Forster saved the Brazilian’s long-range effort with ease and was similarly comfortable behind efforts from Roberto Firmino and Emre Can, the only other attempts of any note in the opening 45 minutes.
The hosts were ponderous and lacking cutting edge, and Southampton’s defence was barely troubled, while Claude Puel’s men showed no ambition going forward, per BBC Sport:
BBC Sport @BBCSport
HT Liverpool 0-0 Southampton
#SAINTSFC failed to have a shot in the 1st half for the first time since 2012
It was much the same after the break until Southampton defender Jack Stephens conceded a harsh penalty for handball.
Milner stepped up and fired low towards the left corner, but Forster got down brilliantly with a strong right hand to keep the score level, per football writer Duncan Castles:
Duncan Castles @DuncanCastles
Very hard to understand how the referee sees an intentional handball there.
Justice done courtesy of Fraser Forster. #LIVSOU
Saints seemed galvanised by the save and became more adventurous in attack, forcing two corners that troubled Liverpool’s shaky defence.
Reds manager Jurgen Klopp introduced Daniel Sturridge and Adam Lallana on 69 minutes, and the former quickly made an impact, opening up space in the box with quick feet.
But he could only poke a tame finish at Forster 12 minutes from time, and as the game opened up, Liverpool looked as though they may be punished on the break by the visitors.
Reds goalkeeper Simon Mignolet was lucky to escape unpunished after rashly coming off his line to collect the ball at the edge of the box late on. And Forster made another key save in stoppage time from substitute Marko Grujic.
In the end, it was a game that arguably did not deserve a goal, and Liverpool are again in danger of dropping out of the top four.