"It was a very good game which deserved fans. With a bit more clinical finishing we should have finished the game. They were there for the taking," Solskjaer said.
"We had some big chances. The difference when you get to the big games is the clinical moments," he added.
United's Brazilian midfielder Fred was sent off in the 70th minute after a first-half booking for an off the ball head-to-head clash which had made him a likely candidate for a halftime substitution.
Solskjaer said he had considered replacing the Brazilian but felt the dismissal was harsh.
"Fred has played really well. We spoke about staying calm and on your feet. The second yellow card was nowhere near a foul. Ander [Herrera] knows that," he said.
United, PSG and RB Leipzig are now level on nine points with Solskjaer's side facing a tricky test in Germany on Tuesday.
"The destiny is still in our hands. If we go to Leipzig and win the game we go through. We want to be in the Champions League and we need to show that next week with a good performance," he said.
United captain Harry Maguire felt his team had been unlucky.
"We had better chances. Their two goals are scrappy goals -- ricochet and pinball around the box. I feel we deserved something," he said.
"You've got to take your chances and not give away soft goals. But we're still in control of going through to the knockout stages."