Manchester United’s troubled season took another turn for the worse as they slipped to a 2-0 defeat at Liverpool and faced up to the loss of Marcus Rashford for between two and three months.

Ole Gunnar Solskjær reported that Rashford had sustained a stress fracture in his back after taking a heavy knock in the 1-0 FA Cup replay win against Wolves at Old Trafford last Wednesday. United’s manager described it as “a bad injury”.

Rashford’s injury has clear implications for the England manager, Gareth Southgate, who is preparing for the Euro 2020 finals that begin in June. Southgate has already lost one of his other main strikers, the captain Harry Kane, to a serious hamstring injury.

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Kane is out until mid-April, at best, but his manager at Tottenham, José Mourinho, has suggested he may miss the remainder of the season. England play warm-up games against Italy and Denmark in late March.

Solskjær said in his pre-match interview at Anfield that Rashford, who also has an ankle injury, had “aggravated his back [against Wolves]; he has had trouble [there] before” and it was easy to question his decision to introduce Rashford against Wolves, which he did when the score was 0-0, albeit hindsight is a wonderful thing.

Solskjær insisted Rashford had not been carrying the stress fracture before the Wolves game and that it was the result of the challenge from Matt Doherty. He appeared to confirm Rashford had a double fracture and ruled him out for a minimum of six weeks but added that after this the player would need “some recovery or rehab”.

Solskjær said: “Marcus suffered a stress fracture against Wolverhampton. I don’t know how long he will be out. We will give him enough time to heal. It’s normally six weeks before you get going slightly, probably, and then he will need time to get match-fit again.”

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Solskjær was asked whether Rashford had one of the fractures before the Wolves replay. “No,” he replied. “It happened, both of those ... I don’t want to go into too much detail but it happened in that game. We’ve just got to deal without him for a while. He’s been absolutely fantastic all season. We had a similar spell with Anthony Martial out for eight weeks and Mason Greenwood got a few more games, he has got more experience. We’ll just have to deal with it.”

United want to make additions during the transfer window and are trying to close a deal for the Sporting Lisbon midfielder Bruno Fernandes, among others. Solskjær has long-term injuries to other key players, namely Paul Pogba and Scott McTominay.

“The permanent signings we’re looking for – the targets are not going to change because we’ve got two or three players injured for the next few months,” Solskjær said. “There might be some short-term deals we have to do. But today is not about the transfer window, it can’t be. We’ve just had a game against the best team in the country.”

Jürgen Klopp saluted his team’s victory, which ended with the Kop singing about winning the league. “Everyone should celebrate the situation, apart from us and we have no problem with that,” he said. “All of the boys played an exceptional game. It is a wonderful performance against an opponent with the quality of United, who made it difficult.”