"We cannot compare with their intensity," Mourinho said. "We cannot compare with their physicality."
The sight of former United manager Alex Ferguson looking glum in the stands and record United signing Paul Pogba burying his head in his thick training top to shield himself from the driving rain summed up the state of United at the moment.
"We can still finish fourth," said Mourinho. "For sure, we are going to finish top six."
United is one point above seventh-placed Wolverhampton and 11 behind fourth-placed Chelsea.
Shaqiri's intervention spared Liverpool goalkeeper Alisson Becker from some embarrassment after the Brazilian gifted United their equaliser by fumbling a fairly tame cross from Romelu Lukaku into the path of Jesse Lingard in the 33rd minute.
That goal cancelled out the 24th-minute opener from Sadio Mane, which came amid a breathless start from Liverpool as United's defence was opened up constantly.
"The mix-up of big fight and really playing football against an unbelievably strong team," Liverpool manager Jurgen Klopp said of his team's performance, which he described as "one of the best we've had" in his three-year tenure.
Liverpool reclaimed their one-point lead over Manchester City with nearly half the season gone.
United, meanwhile, are on 26 points - their lowest haul after 17 games since 1990-91 - and have a goal difference of zero.
• Eden Hazard is settling just fine into his new attacking role at Chelsea. Playing as a false nine for the second straight game, Hazard set up Pedro Rodriguez's early goal and then scored himself for the first time since October to lead Chelsea to a 2-1 win at Brighton.
The Belgium forward usually plays on the left but is being deployed by manager Maurizio Sarri in the centre of a mobile front three, between Pedro and Willian. It was an approach Sarri used to great effect when previously in charge of Napoli.
Hazard set up both goals in Chelsea's 2-0 win over Manchester City a week earlier, leading Sarri to keep him as the team's deep-lying central striker at Brighton.
Outplayed in the first half, Brighton improved after the break and reduced the deficit when Solly March turned in a shot from close range in the 66th minute.
• The drinks were on Ralph Hasenhuettl at St Mary's Stadium. In a bid to raise spirits at struggling Southampton, their new Austrian manager sent drinks vouchers to all season-ticket holders ahead of the game against Arsenal. It wasn't the only thing Saints fans were celebrating yesterday.
Charlie Austin's 85th-minute goal sealed a 3-2 win that lifted Southampton out of the relegation zone with 17 of 38 matches gone. It was the first victory for Hasenhuettl since replacing Mark Hughes two weeks ago, and he greeted the final whistle by running on to the field and leaping into the air in delight.
Arsenal twice came from behind through goals from Henrikh Mkhitaryan and looked like preserving a 22-game undefeated streak in all competitions (14 in the league) stretching back to August 18. Danny Ings put Southampton ahead both times. Arsenal stay fifth, now three points behind Chelsea.
- AP