Nemanja Matic insists Manchester United are where they belong after climbing to the top of the Premier League following their 1-0 win at Burnley.
United moved into a three-point lead over Liverpool that could immediately be wiped out, with Solskjaer's side heading to Anfield on Sunday.
Solskjaer won six Premier League winners' medals during his time as a player at Old Trafford and was glad his side regained focus after a heated end to the opening period.
"It is [big] and you know even for us and the fans it is great, but there is a long way to go".
The great Alex Ferguson was still in charge the last time United led the standings this deep into a league campaign.
"Of course we know we're going to the champions who have had an unbelievable three-and-a-half-seasons", said Solskjaer.
"We could not have asked for a better time to play them because we are in good shape, good form. He's getting better and better every game". When you look at where they were against Tottenham at home and where they are now.
Shaw, who was booked for his hefty challenge on Johann Berg Gudmundsson, soon swung in a cross that Harry Maguire headed home from an acute angle, only for it to be ruled out for a push by Maguire on Erik Pieters as he climbed.
Pogba himself could have won a penalty in the second half after being shoved in the box.
Carlo Ancelotti was forced to start without a recognised striker without Dominic Calvert-Lewin and Richarlison only fit enough for a place on the bench.
"I thought we were in control and confident on the ball and it was a deserved win".
"But I think today we showed more maturity, we showed we are more clever".
The Blades still face an uphill task to haul themselves off the bottom of the table as they sit nine points adrift of safety.
But Chris Wilder's men ensured they will not set an unwanted record by going a full top-flight season without a win thanks to another night to forget for Newcastle. "It looked like we got our identity back", Wilder said.
United pushed to get this game in hand played this week, and going into Anfield with a three game advantage may turn out to be a masterstroke for the players' confidence.
The Magpies could yet find themselves dragged into a relegation battle as they remain eight points above the drop zone in 15th, but have played two games more than Fulham in 18th.