Solskjaer struggled to hide his frustration on Sunday after his side were controversially denied a first-half penalty in a goalless draw at Chelsea.
The United manager later claimed that officials are under pressure not to award spot-kick to his side due to comments by the likes of former Chelsea manager Frank Lampard and Liverpool’s Jurgen Klopp.
Solskjaer also took aim at Chelsea for publishing an article on their club website which drew attention to an incident involving United captain Harry Maguire and Cesar Azpilicueta in October.
The Norwegian has always been reluctant to engage in verbal sparring with managers at United's rivals, turning down one such opportunity before meeting his predecessor Jose Mourinho and Tottenham earlier this season.
And when asked whether he may need to retaliate in order to protect his team, he refused, insiting that he would rise above the psychological warfare.
"No. I believe in… how can I say it… fairness, karma and I’m just made the way I am," Solskjaer said. "I will make it despite of, not because of. That’s just me. We’ll get through it. Don’t worry about that."
Second-place United travel to Crystal Palace on Wednesday night before a shorter trip to runaway leaders Manchester City this weekend.
Solskjaer wants his players to be ready to take advantage if an imperious City side slip up between now and May, and likened their chase to Jackie Stewart's first win as a Formula One driver.
Stewart won the 1965 Italian Grand Prix after leader Jim Clark suffered a mechanical breakdown on the final few laps and team-mate Graham Hill made a wrong move while close to the finish.
"That’s just what we have to do. We have to go all the way. Don’t think about City, don’t think about the points tally. You’ve got to go every single game step by step," Solskjaer said.
"Jackie Stewart’s first win in Formula One. I think we’ve all heard about that one. You never know what’s going to happen in life and definitely not in football and sports.
"Do our job and don’t have any regrets when the season is over - just pick up as many points as we can, play as much as we can and improve as much as we can."