An intense encounter between the two Roses rivals at Elland Road served up few goal-scoring chances and failed to live up to its pre-match billing.
“Today we just didn’t have the moment, take (our chances) when we had them,” Solskjaer said.
“A draw is disappointing because we wanted to put pressure on (Manchester) City, but we couldn’t score.”
Solskjaer’s side, 10 points behind City with five games to play, extended their unbeaten Premier League away run to 24 matches and are now undefeated in their last 13.
Leeds’ first top-flight home game against their old foe since 2003 was overshadowed by the European Super League’s attempted coup.
Solskjaer said none of his players or staff had seen the banner flown above Elland Road before kick-off, which read: “£2bn stolen #GlazersOut”.
The Norwegian said the fall-out from the ESL’s failed bid to hijack the Champions League would not be a distraction.
“I’m really happy with the boys’ focus,” Solskjaer added. “They have such a determination to finish the season strong.
“So we’re very focused to do well against Roma (in the Europa League) and then we’ve got Liverpool in between, so I’m not worried about that at all.”
There were no fan protests before the game. Manchester United supporters had gathered at Old Trafford on Saturday to vent their anger, while Leeds fans had protested before Monday night’s 1-1 draw against Liverpool.
In Sunday’s encounter, Marcus Rashford’s first-half free-kick was superbly saved by Illan Meslier and Leeds winger Helder Costa’s second-half shot was deflected over the crossbar.
Those efforts were the closest either side came to scoring, but Leeds boss Marcelo Bielsa was delighted with his players’ efforts after the point lifted them above Arsenal into ninth place.
“It was a very demanding game for us,” Bielsa said. “For the game not to become unbalanced, the team made a massive effort.
“Even if they dominated in the main, we managed the chances on goal similarly and even if they did have more of the ball to attack and they had a lot more attacks than we did, I insist I value everything we did so the game would not become unbalanced.”
Leeds are now undefeated in six Premier League games for the first time since 2002, a run that has also included draws against ‘big six’ sides Chelsea and Liverpool and victory at Manchester City.