Solskjaer guided United to an eighth straight win with a 3-1 victory over Arsenal in the FA Cup last night.
Goals from Alexis Sanchez, Jesse Lingard and Anthony Martial secured Manchester United’s path into the last-16.
United fans have not been so buoyant in years and a top-four spot to salvage the season is now a real possibility.
And Solskjaer reckons United have finally got their identity back.
“Today we looked more like a proper team. We looked more structured. We’d worked hard at defending and counter-attacking.
“Counter-attacking is classic Manchester United – Wayne Rooney, Cristiano Ronaldo, Ji Sung-park – we’ve scored so many at Arsenal over the years.
“Today was a big step forward. It was a massive improvement from the Tottenham game.
“It’s easy to get excited and talk about the future but we need to just keep working and think about the next game.
“We had to dig deep. The attitude and work-rate was important. Towards the end it was comfortable but not during the 90 minutes.”
Sanchez and Romelu Lukaku both started for United at the Emirates despite missing out in recent weeks.
Sergio Romero also impressed in goal with Lukaku laying on assists for the opening two goals.
And Ole Gunnar Solskjaer has faced major issues when deciding who to pick, but knows it’s not the worst problem to be confronted with.
“It’s fantastic to go through in the cup,” he told BBC Sport.
“It’s one of the hardest games you can get.
“I’ve had a [selection] headache since I came because the squad is full of good players.
“It’s up to us to pick the right tactics and players. We need to rest a few as there’s big games coming up. But we have fresh legs.”
Pundit Ian Wright has praised the United players, who have shone since Jose Mourinho was sacked last month.
He said: “Manchester United look like different players.
“The way they are playing, they couldn’t have been enjoying it under Jose Mourinho at the end.
“We’re seeing tremendous performances. Arsenal were trying to score a perfect goal but they just needed to get the ball into the box more.
“I was thinking at some stage were Arsenal going to drop back a bit but it never happened.
“They did deserve it tonight United, it was a poor performance from Arsenal.”
As for Arsenal, manager Unai Emery admitted his side were outplayed at home.
“They have been clinical over the 90 minutes. We had chances but couldn’t score and thats the difference,” he said.
“I hope they are not two big injuries. Our game plan worked well, we had pressure and chances but in the second half we can take some risk.
“The players worked well to win this match but we lost today. We deserved more.”