Solskjaer was left frustrated after seeing two penalty claims turned down in the 2-1 win over West Ham in the Premier League on Sunday and another in 1-0 defeat to David Moyes' side in the Carabao Cup on Wednesday.
Klopp questioned the number of penalties awarded to United ahead of a game between the two teams in January and Solskjaer believes the comments have had an impact.
Klopp said following Liverpool's 1-0 defeat at Southampton in January: "I hear now that Manchester United had more penalties in two years than I had in five-and-a-half-years. I've no idea if that's my fault, or how that can happen."
And Solskjaer hit back on Friday and said: "We just have to hope we get what we deserve.
"We should have had three penalties in the last two games. There was a certain manager who worried about us getting penalties last year and after that the decisions were difficult to give.
"I've seen a big difference since then on. We have to leave it to the referees to make the right calls."
United are hoping to bounce back after the midweek defeat to West Ham when Aston Villa visit Old Trafford on Saturday.
"Edinson is in the squad," Solskjaer added.
"He's been training and now he feels ready to contribute. He came on against Wolves then he got a slight strain in the international break when we had a game and he's ready again.
"He's worked really hard and diligently and hopefully he'll have an impact as he did last season."
David De Gea is also set to return after starting the season in fine form, including a stoppage time penalty save at the London Stadium.
"He did call me this summer to end his holiday earlier and came back to start his pre-season before planned," Solskjaer added.
"He wanted to be ready, to be the best possible version of himself. Last season was a challenging one for David, he didn't play as many games as normal because Dean [Henderson] came in and did really well.
"David is better physically and mentally. When you feel you've done the work --he got personal bests on quite a few physical tests -- that gives you confidence, inspiration and motivation."