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But on the stroke of half-time, with Liverpool in the ascendency, Nunez had the opportunity to put them in level at the break with a guilt-edged chance.
But the Uruguayan missed, Liverpool went in behind, lost their momentum, and found themselves two down before the hour mark after a lacklustre start to the second period.
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"That is not acceptable at this level, certainly when Liverpool are going for the title."
And Carragher would go further, wondering if, after two years on Merseyside, and 33 goals in 92 games for the club, it might be time for Liverpool to cut ties with the ex-Benfica hitman already this summer.
"I think there is a question to ask," he added.
"You want him to do well because there is so much that you like because he gives everything, he runs and causes trouble and gets the odd goal and gets an assist.
"But after two years when Liverpool this season are going to the title and those big games, you need your man to score away at Old Trafford, away at Goodison, in the European game at Atalanta.
"You are looking at it now and after two years, I don’t think there is going to be a massive improvement in him1
I don’t think it is going to be enough to win you the biggest trophies so I think there is a big decision to be made on him in the summer."
Who will win the Premier League title.
Man City- P32, 73pts (GD +44)
Arsenal's remaining fixtures
Tottenham [A] - Sunday 28 April (2pm)
Bournemouth [H] - Saturday 4 May (12:30pm)
Manchester United [A] - Sunday 12 May (4.30pm)
Everton [H] - Sunday 19 May (4pm)
Manchester City's remaining fixtures
Brighton [A] - Thursday 25 April (8pm)
Nottingham Forest [A] - Sunday 28 April (4:30pm)
Wolves [H] - Saturday 4 May (5:30pm)
Fulham [A] - Saturday 11 May (12.30pm)
Tottenham [A] - Tuesday 14 May (8pm)
West Ham [H] - Sunday 19 May (4pm)
Liverpool's remaining fixtures
West Ham [A] - Saturday 27 April (12:30pm)
Tottenham [H] - Sunday 5 May (4:30pm)
Aston Villa [A] - Monday 13 May (8pm)
Wolves [H] - Sunday 19 May (4pm)
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