MANCHESTER, England — Manchester United is headed back to the Champions League.A 3-2 win against Liverpool on Sunday confirmed United’s return to European club soccer’s top competition after a two-year absence. Kobbie Mainoo settled a thrilling Premier League clash at Old Trafford with his first-time strike from the edge of the area after defending champion Liverpool had fought back from two goals down. The victory saw head coach Michael Carrick achieve the target he was set in January when he was handed the job until the end of the season. Rescuing United’s season from freefall, he has led the club to third in the standings and produced statement wins against Arsenal, Manchester City and now Liverpool. Victory will strengthen calls for Carrick to be given the role on a permanent basis. “When Michael comes, he came with magic. Alex Ferguson vibes,” United forward Matheus Cunha said with reference to the club’s iconic former manager. “At the end of the day, this is just the start of the journey. It’s the beginning, a beautiful beginning.”Ferguson had planned to watch the match at Old Trafford but left the stadium and went to the hospital as a precaution when feeling unwell before kick off. The fact United secured a Champions League return against its fiercest rival Liverpool only added to the scenes of celebration after the final whistle. It was the first time United has completed a league double of home-and-away wins against the Merseyside club since the 2015-16 campaign.United is six points ahead of fourth-placed Liverpool with three rounds of the season to go. It marks a significant improvement on last term when it was 42 points behind Arne Slot’s title-winning team.Since Carrick was hired on Jan. 13, United has picked up 32 points from 14 games – more than any other team in the top flight. “It’s been a good run. We’ve beaten some very, very good teams and it’s been challenging,” he said. “I love doing what I’m doing. It’s a great position for me to be in and it feels pretty natural if I’m totally honest.”United only gave Carrick the job until the end of the season in order to give the club time to weigh up coaching candidates after Ruben Amorim was fired in Ja …