United became the first side to ever overcome a 2-0 first leg defeat at home to reach the last eight with a 3-1 win in Paris last month.
But Solskjaer, who scored the winner when United won the Champions League at the Camp Nou in 1999, believes Barca’s prestigious European history makes beating the Spanish champions a different prospect to PSG.
“Of course the PSG performance away gives us hope and belief we can do it, but we know we are playing against probably the favourites for the tournament,” said Solskjaer.
“It will be a greater achievement winning that one with the history of Barcelona. They are not used to losing at home.”
Luke Shaw’s early own goal was all that separated the sides on the scoresheet, but Barca comfortably edged towards a first Champions League semi-final in four years as United failed to register a single shot on target.
“It leaves a good taste in the mouth to win here, but we know it is not a big enough lead given what happened (with United) in the last round,” said Barca coach Ernesto Valverde.
Much has been made of Luis Suarez’s Champions League goal drought on the road and while the Uruguayan has still not officially netted an away goal in the competition since September 2015, he had a huge hand in Barca’s winner.
Lionel Messi drifted in behind the United defence and his cross hung up to the back post was headed goalwards by Suarez, the ball flicking off Shaw on its way past David de Gea.
An errant offside flag briefly threatened to spoil Suarez’s delight. However, the goal was quickly given on a VAR review and the former Liverpool striker took extra glee at having the last laugh with a fist pump in front of the Stretford End.
“The value of the goal doesn’t change if another player gets the last touch or not,” added Valverde.
The early goal should have settled the Catalans into their stride as their dominance of possession touched close to 90 percent in the opening stages.
Yet they offered United plenty of encouragement with Sergio Busquets in particular off the pace.
“It is very difficult over the course of a season to always be at the highest level,” said Valverde.
“To win away from home in the Champions League you have to suffer.”
United defender Chris Smalling had said “bring it on” at the prospect of facing Messi on the eve of the game.
And he left the Argentine bloodied from the nose as he careered into an aerial challenge on the half-hour mark.
Messi was quickly back on his feet and into the heart of the action, but it was Philippe Coutinho who came closest to extending Barca’s advantage before the break with a thunderous low shot that De Gea did brilliantly to repel with his feet.
Moments later United could easily have been on level terms, but the hosts’ best chance of the half fell to the wrong man as Marcus Rashford picked out Diogo Dalot only for the Portuguese to completely miscue his header across goal.
However, Rashford also failed to make proper contact with his big chance early in the second-half when Ter Stegen could only punch a cross into his path.
The Red Devils have now failed to score and have lost in four of their last six home Champions League games.
“Those statistics are not bright, we cannot defend not scoring goals at home,” added Solskjaer.
“But away from home we beat Juventus, we beat PSG and we have to go to Barcelona and win that one.”
The result could have been worse for Solskjaer’s men as Suarez fired into the side-netting before De Gea used his feet to good effect once more to deny Jordi Alba.