The Hammers avenged their defeat against the Red Devils in the Premier League last Sunday and Solskjaer has defended his men’s display.
The visitors took the lead nine minutes into the game through Manuel Lanzini and that was enough to book a fourth round game against United’s local rivals Manchester City.
Solskjaer’s men had a lot of opportunities to equalize but passed up glorious chances as they mustered 27 shots throughout the game.
In an interview with the media after the game, the Norwegian coach defended United, as he thinks they did enough to give West Ham a competition.
"Lacking a goal. A slow start again and that needs addressing. They got a goal and after that we played well for long periods, gave it a go and stats don't mean anything. When you have 27 shots it means the boys have given it a go,” Solskjaer said.
"We built pressure, Mason Greenwood came on and had a good one but sometimes the pressure does not come to anything. He made a positive impact, he was fresh and sharp but it was too little too late. The last six or seven minutes we were going gung-ho and they could have scored a couple.
"I would rather not say too much but it was a penalty again on Jesse Lingard.
"You want to go through but it is a long season, we gave it a good go, can't fault them for attitude and have big games coming up.
"It is a long journey all season, we have loads of games and keep on doing what we are doing, trying to get results. We are out of this cup which is not great but we will focus for Saturday."