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They secured all three points in what was a crucial Group F clash against Villarreal as two second-half goals from Cristiano Ronaldo and Jadon Sancho helped them secure a place in the Champions League last-16.
Solskjaer's former first-team coach couldn't have wished for a better result and after the whistle, Sky pundit and Liverpool legend produced a viral post on Twitter to mark the occasion.
"Manchester United might not thank me, but get the contract out, put it on the table and let him sign it." Carragher wrote on Twitter.
"Let him right whatever numbers he wants, let him sign the contract. Carrick's at the wheel man."
Man Utd might not thank me, but get the contract out put it on the table & let him sign it, let him right whatever numbers he wants, let him sign the contract. Carrick's at the wheel man! #VILMUN @ChampionsLeague
- Jamie Carragher (@Carra23) November 23, 2021
Of course, Carragher's statement is in reference to Rio Ferdinand's iconic speech after United secured a place in the Champions League last-16 following a last gasp win against PSG in 2019.
Ferdinand certainly made it clear that he wanted Solskjær to be appointed on a permanent basis in the BT Sport studio that day.
"Man United might not thank me, but get the contract out, put it on the table, let him sign it, let him write whatever numbers he wants to put on there -- given what he's done since he's come in -- and let him sign the contract and go," he said.
"Ole's at the wheel, man -- he's doing his thing. Man United are back!"
Yessss Ole is officially at The Wheel... Signed, Sealed, Delivered! Manager of @ManUtd! :raised_hands: I hope my Thank You is in post Ole :pencil::heart: #MUFC #Ole pic.twitter.com/lUUel4f6zw
- Rio Ferdinand (@rioferdy5) March 28, 2019
Ferdinand, meanwhile, praised United for a solid, "no thrills" performance against Villarreal on Tuesday night.
"There's no doubt in my mind that in that changing room, they would have been pushing the clean sheet message," Ferdinand told BT Sport.
"This game was about no thrills, discipline and they had a plan. They're the things we've been asking for for weeks and weeks and weeks.
"This wasn't a performance of beautiful, fairy-tale, imaginative football we can all eulogise about.
"It was roll your sleeves up, get into position, be there and be hard to beat. They've done that today."