The Red Devils headed into the game looking to bounce back from the disappointment of their 1-0 loss to Newcastle United before the international break.
Manchester United started the game brightly and took the lead in the 36th minute when Marcus Rashford fired home from close range.
Liverpool FC had a goal chalked off by VAR just before half-time after Sadio Mane was adjudged to have handled the ball before finishing past David De Gea.
The visitors improved in the closing stages of the game and substitute Adam Lallana netted an equaliser for Jurgen Klopp’s men in the 85th minute to earn a point for the Premier League leaders.
Ole Gunnar Solskjaer took over from Mourinho at Old Trafford last December after the Portuguese coach was sacked by the Red Devils.
Mourinho felt that Manchester United should be “proud” of their display against the table-toppers.
“Ole and United, after such a fantastic effort, I think they may feel a bit disappointed with one mistake and two points they lost,” Mourinho told Sky Sports.
“At the beginning of the game, I was asking United for heart. They had it – but [also] more than that. They were organised, they had a game-plan and they stuck to it.
“They couldn’t keep the defensive intensity for 90 minutes. In the end of the game, Liverpool were on top of them and so probably the result is fair.
“If I were Ole, I would be proud and frustrated, because I think the boys gave everything.”
The result left Manchester United in 13th place in the Premier League table with 10 points from their first nine games.
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