The Red Devils have now overcome both Arsenal and Chelsea in the cup after goals from Ander Herrera and Paul Pogba dumped the Blues out at Stamford Bridge.
But there is no let-up for Solskjaer, who now faces seventh-place Wolves in the next round – a team who have already eliminated Premier League leaders Liverpool.
“We have to do it the hard way this year!” Solskjaer told talkSPORT.
“Wolves, the way they set up, with the energy and their playmakers – that will be a tough game for us.
“Then again, we’ve been away to Arsenal and away to Chelsea, so if you want to get to the final you have to win all of them.”
Pogba was United’s inspiration once again during the victory at Stamford Bridge, creating the first and scoring the second as the visitors bounced back from the 2-0 defeat to Paris Saint-Germain on Tuesday.