Solskjaer insisted on Saturday night that his players could only blame themselves for the opening day 3-1 defeat to Crystal Palace. So he is likely to take a dim view of Shaw’s words.
The left-back said: “We have a very good group, but personally I think we need more players to strengthen the squad.
“It can give us a boost. When you look around at how other teams are strengthening their teams, then we must also do it to keep up with the others."
Donny van de Beek is United’s only new signing after Solskjaer secured a return to the Champions League last season.
The Norwegian is still hopeful of landing top target Jadon Sancho, while left back Alex Telles is closing in on a move from Porto.
The United manager said on Saturday: “We can play so much better than today. If you look at the players we have on the pitch and on the bench and not here we have to look within first and know we can perform better.
“It was an off day, everyone knows they can improve and we will improve. But we are always looking to improve if there is something available at the right price.”
Shaw added after the shock defeat: “Possibly everything went wrong. Personally from my point of view the pre-season that we’ve had all together is not the correct way it should have been, we’ve had a week all together.
“We haven’t been able to prepare in the way that we wanted and that’s not an excuse because we have the quality of players to be able to win games like this, but we weren’t up to it tonight and we’ve been punished.
“It’s the start of a new season, we should have been fresh. We knew how Palace were going to play, sit in the block and try to stay on that, possibly all of their goals came from that.
“We paid the price today and at times we were sluggish and weren’t at it and like I said we paid the price.”