Arsenal stayed fourth, although Tottenham Hotspur will have a chance to push them back into fifth when they play away at Wolverhampton Wanderers later on Saturday.
During the eight-game unbeaten league streak prior to the Liverpool draw, there were tentative questions regarding Arsenal's title credentials.
Klopp's side took the lead on the hour mark, though, as Leno pushed Mane's cross back in front of his own goal, with Milner on hand to drill in his third of the season.
"We got dominated at times in the first half but we still got the first goal and that shows we are capable of still producing when we've been under pressure".More news: Black Box Found From Crash of Indonesian Passenger Plane
The Senegal global tapped home after Roberto Firmino had hit the post but his effort was chalked off even though he was behind the ball, having initially been offside when the move started.
"We've just got to keep ticking away with the points and you never know what can happen further on in the season".
Emery felt his side's performance against Liverpool highlighted the progress they have made in recent months.
Arsenal's 1-1 draw against Liverpool seems to have convinced a lot of persons about the ability and impact of the Gunners manager Unai Emery on the team. But perhaps that isn't entirely fair for Liverpool; after all, this is an Arsenal side that has improved significantly since then, one riding a 14-game unbeaten streak.
"We could have kept our shape better in the first half".More news: 7 killed in Egypt as bus carrying Christian pilgrims is ambushed
Granit Xhaka fired too close to Alisson from a well-worked corner, but the Brazilian worldwide was fortunate when he rushed from his goal and was beaten to a floated cross by Henrikh Mkhitaryan, whose header drifted inches wide.
Lacazette was proving to be troublesome for the Reds and he smashed a low shot just wide before beating Alisson from close range, only for Shkodran Mustafi to be given offside in the buildup.
Arsenal might well have gone behind before James Milner's 61st-minute strike and perhaps should have trailed at the break.
A dubious offside decision denied Sadio Mane the opening goal and Virgil van Dijk twice should have scored when he was first repelled by Bernd Leno and then flicked a header against the post with the German 'keeper caught flapping. He broke up play judiciously, gaining possession 15 times without ever resorting to the rashness that makes for a weighty disciplinary record.More news: 'Vote your values': Oprah Winfrey campaigns for Stacey Abrams