The Red Devils have reached transfer deadline day having made three additions to their ranks.
Maguire has joined Daniel James and Aaron Wan-Bissaka at Old Trafford, with there the potential for more deals to be done before the summer deadline passes on Thursday.
Former United defender Parker believes more proven performers are required in order to make Solskjaer’s side competitive, with the club having overspent in one area and failed to address their deficiencies in another – with Romelu Lukaku’s proposed move to Inter set to leave them short in attack.
“Ole Gunnar Solskjaer is under a lot of pressure. He needs a good start and he needs his team to show consistency. People are questioning how that team fell apart after such a good start,” Parker told Eurosport.
“They capitulated - their performance at Everton (a 4-0 defeat in April) was like an ostrich sticking its head in the sand, it was awful. So Ole is under immense pressure.
“United have addressed a situation that the fans have been screaming for. They've been saying that their centre-halves are rubbish, which was implanted in people's heads by Jose Mourinho.
"The best way to shut the fans up is to go and spend £80m on a defender who everyone knows is not worth that money.
“The hope is that Harry Maguire can have the same impact that Virgil van Dijk has had at Liverpool, but you rarely get two bangs out of a stick of dynamite. I really don't see how Maguire is going to come out and play in the same vein as Van Dijk. They're hoping that he can make the defence better, but there's a massive amount of pressure on him.
“United still have problems elsewhere, in midfield where there's a lack of creativity. There's been talk of Christian Eriksen coming in there, and then upfront, Romelu Lukaku wasn't the ideal frontman that United need.
“If you take Lukaku's goals away, there wasn't enough substance. They need another centre-forward as at the moment they've not got anywhere near enough, they can't rely on what they've got unless someone hits the ground running and keeps at that pace throughout the nine months of the season.”
United are being linked with a number of frontmen, including Juventus star Mario Mandzukic, but face a race against time to get bodies on board before attention turns to the start of the 2019-20 Premier League season.