De Gea has made a number of uncharacteristic mistakes in recent games but Solskjaer says the goalkeeper cannot take the blame for the team's struggles.
"I don't have any worries about him, because he's a strong character," Solskjaer told British media. "He knows he could have had that shot, but that's football."
The result leaves United sixth in the league on 65 points and dented their hopes of securing a top-four finish. They sit three points behind fourth-placed Chelsea with two games left.
"With David, he's been in the spotlight for right reasons for so long and now he's going through a period where he feels he could have done better," Solskjaer added.
"But there's no chance any of us will point fingers because he's saved us so many times. I'll speak to David, as I've done when he's played well... he's not the reason we're sixth."
United's last two games of the season are against Huddersfield Town and Cardiff City.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford)
