“Paul always has a point to prove because he wants to be the best,” said Solskjaer. “He’s had such a frustrating season with his injuries.
“For me, Paul has shown today how he can contribute. I just look forward to getting him fitter so he can get back to his best.”
A point does little for either side’s chances of breaking into the top four.
United remain in fifth, two points behind Chelsea, but Spurs were even more desperate for the points as they remain in the eighth, four points further back.
Jose Mourinho was on course to get the better of his former club when Steven Bergwijn’s strike gave Spurs a half-time lead.
Fernandes then thought he had won a second penalty, but a VAR review decided there was little contact as he went down under another challenge from Dier.
“We know Manchester United has an incredible record this season of penalties given, so we knew everything in the box was dangerous for us,” said Mourinho.
“I think in the first penalty, the referee made this decision which I admit is difficult for referees, but then the VAR is a different story.
In keeping with all matches since the Premier League’s return earlier this week, all players and officials took a knee before the kick in protest against racial injustice.
Once the action did get underway, United settled quickest to the eery surroundings of a 62,000 seater stadium draped in banners with the only fans appearing on giant video screens behind each goal.
Marcus Rashford has had a momentous week as the English international’s campaign to ensure vulnerable children are not left without food vouchers during the English school holidays forced a government U-turn.
Solskjaer described the 22-year-old’s action as far “more important than any game of football that he would probably play.”
However, the England international admitted he was also desperate to get back to the day job after being sidelined since January with a back injury prior to the coronavirus-enforced shutdown of football for three months.
Rashford had the best chance to turn the visitors’ early control into a goal as his low shot was beaten away by the legs of Hugo Lloris.
Prior to lockdown, Mourinho spoke of his desire to fast forward to the end of the season when he would have Harry Kane, Son Heung-min, Moussa Sissoko and Bergwijn fit again.
Bergwijn surged past the leaden-footed Harry Maguire before David de Gea could only parry his powerful shot into the roof of the net.
Tottenham sat on their lead after the break and invited plenty of United pressure.
Lloris kept United at bay with an incredible save to deny compatriot Anthony Martial.
The midfielder’s quick feet left Eric Dier in his wake and Dier then pushed Pogba over inside the box as he tried to recover.
Fernandes coolly sent Lloris the wrong way from the penalty spot to deservedly level and moments later went down himself inside the box.
Jon Moss pointed to the spot again, but Rashford’s chance to score the winner was taken from him as this time the VAR call went Mourinho’s way.