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It was a sublime display by Arsenal who wiped off a goal difference deficit to champions Manchester City who they joined on 52 points, although they stay in third place courtesy of scoring fewer goals.
Liverpool won 3-1 while Manchester City beat Everton 2-0 in an earlier match.
Liverpool, beaten by Arsenal on Sunday, lead the table on 51 points from 23 games but City are up to 49 from 22 and Arsenal on 49 from 23.
"Congratulations to Arsenal. We were not good enough today," Klopp said. "It just shows the boys are human beings."
Liverpool moved five points clear atop the Premier League to set up a potential thriller on Sunday against third-placed Arsenal.
Fourth-placed Aston Villa suffered a 3-1 home defeat by Newcastle United, Crystal Palace came from behind to beat visiting Sheffield United 3-2 and struggling pair Fulham and Everton fought out a goalless draw at Craven Cottage.
The German joined Liverpool in October, 2015, and has won the Champions League, Premier League, Club World Cup, FA Cup, League Cup and Super Cup, as well as the Community Shield during his time in charge.
Uruguayan Nunez put the seal on a dominant Liverpool display with his second goal in stoppage time.
City have 43 points from 20 games with Liverpool on 45 while Newcastle's fourth successive defeat left them 10th in the standings.
While Liverpool's 7,000 travelling fans celebrated, Arsenal's left the Emirates Stadium chuntering about the need for a new striker in the transfer window.