The Serie A side lost the semi-final 7-6 on aggregate despite winning the second leg 4-2 in Rome.
And Pallotta felt his side should have been awarded two penalties.
“I know it is difficult to ref but it is really embarrassing that we lose on aggregate like that,” he said.
“You just can’t let stuff like this happen.”
Edin Dzeko was brought down by Liverpool goalkeeper Loris Karius after the interval but the former Manchester City striker appeared to be wrongly ruled offside.
And minutes later Trent Alexander-Arnold handled the ball in the area which denied a clear goalscoring opportunity for the hosts.
“You can all look at it yourself. In the 49th minute he wasn’t offside and he gets taken down by the goalie,” Pallotta added.
“It was a handball that was obvious to everyone probably in the world except people on the pitch. It should have been a red card which would have been 10 men in the 63rd minute.
“If they don’t get VAR in the Champions League, it is an absolute joke.”