The Premier League giants earned a point from their trip to Stamford Bridge and managed to remain second in the league table.
Both teams were restricted to only a few chances in the game and there were suggestions that both sides were content to take a point from the game.
But Solskjaer insisted that Manchester United wanted to win, but admitted their play in the final third, especially the final pass, let the team down.
He admits that the quality of the game was not great, but insisted that Manchester United still played some good stuff and created a few good chances during the game.
Solskjaer told the BBC’s Match of the Day programme: “We wanted to win.
“Apart from the last quality or pass being not good enough… we had great pressing, desire, and work-rate.
“There was a great save by David de Gea and we got the clean sheet.
“That’s what let us down, that quality on the ball.
“The first half was scrappy.
“Poor game really. But then we played some good stuff at times.
“When we settled we created a few chances but we didn’t have enough.”
Manchester United will be in league action on Wednesday night when they host Crystal Palace at Old Trafford.