However, the Red Devils interim boss was less than impressed with the penalty decision which secured a 2-0 win for Arsenal as they leapfrogged United into the top four.
It was Solskjaer’s first defeat in 13 Premier League outings since he was appointed interim manager at Old Trafford following the departure of previous boss Jose Mourinho in December.
In the 12th minute De Gea, pictured, was caught out horribly by a swerving shot by Gunners midfielder Granit Xhaka which wrong-footed the Spaniard before hitting the back of the net.
United hit the woodwork twice but midway through the second half referee Jon Moss awarded a penalty to the home side after Alexandre Lacazette went down under minimal pressure from midfielder Fred.
Pierre-Emerick Aubameyang, who had missed a last-gasp spot-kick at Spurs last week, confidently tucked away the chance from 12 yards to double Arsenal’s advantage.
Even Gunners boss Unai Emery admitted the decision was “soft”, and Solskjaer said: “I don’t think it’s a penalty but that’s a decision he’s made. I don’t think there’s enough contact there to warrant a penalty.
“It’s not a dive but apparently Fred is very, very strong!
“I don’t class it as a mistake by De Gea. I was stood right behind the ball and we don’t put enough pressure on Xhaka, who must be Brazilian by the way because he struck the ball and it swerves and moves.
“It goes to David’s left and changes direction completely. It’s one of those things.”
Arsenal are now only a point behind Spurs in third and two ahead of United, who lie fifth with Chelsea a point further back.
“Spurs lose, we lose, Chelsea draw, it’s going to be down to the wire, the last few games definitely,” added Solskjaer.
“But we’ve given ourselves a great chance to be in that fight. Three points behind third, two behind fourth, it’s a good position to be in.”
Arsenal keeper Bernd Leno made two fine saves to deny Romelu Lukaku, while the Belgian striker and Fred both hit the woodwork.
Gunners manager Unai Emery said: “I don’t know if it was the best performance this season but we are improving, and being competitive in different matches. We can feel very proud of the players.
“I’ve only been here one year and Xhaka is a specialist with shooting and he can shoot from different positions on the pitch.
“He can shoot far from the goal but his shooting is very dangerous usually. Today he tried to shoot and he scored but I think he can do more and can try like that in each match.”