Premier League United lost 2-0 at Old Trafford and they face an uphill battle on Wednesday to reach the quarter-finals as PSG have only lost one game at home this season -- a French League Cup quarter-final two months ago.
In Ligue 1, they have won all their 14 home games, scoring 50 goals and conceding five while they won two and drew one at home in the Champions League's group phase.
"The players have been fantastic away from home," Solskjaer, whose side have won all eight away matches under the Norwegian, told a news conference.
"We've beaten Arsenal, Chelsea and Tottenham away from home which gives us belief we can do this as well."
Solskjaer said it will be crucial for United to score first.
"It's a difficult task but we can do it," he said. "We need to get the first goal and then we need to stay in the game, because if there's only one goal in it anything can happen. We need a good plan and we need to perform on the night."
United travel to France without several key players as midfielder Paul Pogba is suspended while Nemanja Matic, Ander Herrera, Juan Mata, Anthony Martial, Jesse Lingard and Alexis Sanchez are all injured.
Eight players who have represented the youth academy feature in their squad.
"Every young player at this club is dreaming about coming on and having the impact Rashy (Marcus Rashford) has had," said Solskjaer. "There's been so many examples of that and that's the belief they must have to make it."
Solskjaer promised United would play with pride.
"Everyone expects us to go out easily but that doesn't happen with Manchester United," he said. "Our pride was hurt last time we played them so we are going to see players who are going to give their all."
(Reporting by Julien Pretot; Editing by Toby Davis)
