The United boss saw star man Cristiano Ronaldo have strong appeals waved away during last weekend’s 2-1 Premier League victory at West Ham and another fall on deaf ears when the sides met once again in the Carabao Cup in midweek.
Asked if Ronaldo might have an issue with referees, Solskjaer added: “We just have to hope that we get what we deserve. I believe we should have had three penalties in the last two games.
“I don’t know, but there was a certain manager last year that who was starting to worry about us getting penalties and after that, it seems like the decisions are more difficult to give. Surely I’ve seen a big, big difference since then on.
“But we just have to leave it up to the refs and hope that they will make the right calls very soon.”
Ronaldo, 36, has made an instant impact since returning to his former club from Juventus this summer, scoring four times in his first three appearances to leave himself a marked man, and Villa boss Dean Smith has spoken about his excitement at the challenge of trying to stop the Portuguese superstar.
Asked if that was something his former United team-mate would have to get used to, Solskjaer replied: “Cristiano has been used to that ever since he came to the club, but maybe more so in say the last 15 years of his career.
“His first few years, I think everyone wanted to try to kick him because they wanted to stop him, and then he became such a top player that all the teams would have to have an eye on him.
“His record shows already what an impact he has had with us and he is ready for that challenge. He’s so used to it, so no worries.
“But we’re a team, we know we’re more than just Cristiano and the players that I’ve got to choose from, if they have too much of an eye on Cristiano, there might be space for others.”
Solskjaer, who will have Uruguay striker Edinson Cavani back in the squad this weekend after a muscle strain, has been hugely impressed by Ronaldo’s contribution on and off the pitch already, but knows there will come a time when he has to take a break.
He said: “Of course he knows he’s not going to be able play every game, but that’s a good chat for him to have with me when he feels like he won’t be ready.”
Meanwhile, Solskjaer had saluted keeper David De Gea, who marked his return to top form with a last-gasp penalty save from Mark Noble to ensure United left the London Stadium with the three points last Sunday.
He said: “He did call me this summer to end his summer holiday earlier and come back and start his pre-season before because he wanted to be ready, he wanted to be the best possible version of himself.
“Of course, last season was a challenging one for David as he didn’t play as many games as he’d normally done, but David has really worked, he’s been so focused.
“Physically he’s better, mentally he’s better and when you feel that you’ve done the work, you get personal bests on quite a few physical tests, that gives you confidence and gives you more motivation and inspiration.”