WATCH: Sevilla knocks out Man United to reach UEL final

Solskjaer wants to strengthen the depth in his squad and bring fresh quality into his starting XI, having already seen what an impact just one player of the right calibre can make with the arrival of Bruno Fernandes.

Fernandes – the January arrival from Sporting CP – scored an early penalty against Sevilla but Suso and Luuk de Jong hit back to give the Spanish side a 2-1 success in Cologne on Monday (AEST).

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United has been long linked with Borussia Dortmund and England attacker Jadon Sancho, but Solskjaer refused to discuss that prospect.

Whoever arrives at Old Trafford must fit the profile Solskjaer wants, with the Norwegian reluctant to make any compromises.

"It's going to be a strange summer," Solskjaer said. "We've only got a couple of weeks away from each other until we get going again. That's going to be a mental challenge.

"We're going to keep pushing and keep demanding more of the players we have but still we're looking to improve.

"It's strange - the league starts very quickly but then the market's open for so long. We've got to be good, smart and clever.

"I cannot say when or if transfers are going to be done, but we are of course looking at it. We'll have to sit down because it’s a quick turnaround and we've got to be 100 per cent sure when we make those deals."

The new season will begin in September, but the transfer window will be open until October.

Solskjaer believes United are making impressive steps in the right direction, and a third-placed finish in the Premier League attests to that, given it looked a remote prospect at the turn of the year.

"You can see at times today what we can be about and what we are about," Solskjaer said, after his team dominated large parts of the Sevilla game but could not put the ball away in open play.

He pointed to the 46 shots United have rained in across their games against Copenhagen and Sevilla, while in Germany for the Europa League.

In the Sevilla semi-final showdown, chances were coming at a rapid rate for United, particularly early in the second half.

"But then we seem to let off at times," Solskjaer said. "When we're on top, that's the time to keep squeezing and squeezing at them.

"We let them play too much in periods - 10 or 15-minute spells - and we definitely let them off the hook."

Solskjaer understood why the winning goal from De Jong led to an on-pitch disagreement between Victor Lindelof, who appeared to be at fault, and Fernandes.

Despite making some allowances for a slight deflection, Solskjaer felt the sign of tension on the pitch showed the desire to win in his team.

"Maybe it's a disappointing goal to concede and I want the players to be accountable and to put others to account," he said. "I think it was just a bit of frustration."