Manchester United lost 2-1 at Wolves as Diego Jota and Raul Jimenez put Solskjaer’s side to the sword at Moline.
The win gives Nuno Espirito’s team their first FA Cup semi-final for 21 years and their first cup quarter-final since 2003.
United were poor throughout, although Romero – who replaced David De Gea in goal – made some brilliant saves.
And Solskjaer singled him out for praise on a tough night for the Red Devils.
“Sergio made some fantastic saves – he’s played really well again,” the United boss said.
“But that’s disappointing because they had the better of the chances. They deserved the win.
“Sergio kept us in the game with a fantastic performance from him again but we never put their keeper under pressure.”
United were off the pace throughout, with star men Paul Pogba and Marcus Rashford subdued.
“That’s football for you,” Solskjaer added. “It’s just a slight off on the quality and the tempo of the passing.
“I thought that was maybe the biggest letdown and the urgency, because we are better when we play quickly, we play forward, we run forward.
“A couple of times when Paul [Pogba] broke free in the first half and drove at them, [there were] two yellow cards [for Wolves].
“A couple of times we played Rashy [Marcus Rashford] through the middle, in behind the centre-backs.
“Then if we had the possession, [it was] too comfortable – I think we played it too comfortable.”