The side's captain, Conor Coady, looked back on the journey to reach the milestone of a win over one of the world's biggest clubs, saying: "We have some phenomenal players going forward".
A late Marcus Rashford goal did nothing to lift the mood and the interim manager had no complaints about the his side's exit.
"It was a big step backwards, I have to say".
"That was the poorest performance we have had since I've been here", Solskjaer said.
Solskjaer went on to admit he had ripped into his players in the dressing room as he insisted his players had to bounce back after the upcoming worldwide break.
"This is the poorest we've played, but against a good team".
Asked what he said to the players, the Norwegian said with a laugh: "Well, the truth".
"But of course, you can't sit down and sulk too long".
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"It is a deserved result we were outstanding".
"We've done that quite well".
"I didn't think we had enough quality in the last third, enough combination play". Last week [at Arsenal], we were happy with the performance but, today, we didn't have the urgency or the quality on the ball.
"It is where we all want to be, in two years the club has gone a long way, we are all pulling in one direction, it is an awesome night for everyone".
The 2-1 victory at Molineux thanks to goals by Raul Jimenez and Diogo Jota means Wolves are in the semi-finals for the first time in 21 years and are looking to win the trophy for the first time since 1960.
"What pleases me more is as I walk down the stands there are people saying that they saw the 50s and 60s and they are still coming to the stadium", he said.
"If they hadn't had [David] De Gea behind, then they certainly wouldn't have won as many games as they have". Very well done to the boys and it was a fantastic atmosphere.