The Chilean was enraged by the performance of the officials during his side's heartbreaking defeat at Signal Iduna Park, claiming the host's winner was offside
The Spanish side seemed set to qualify for the semi-finals after Eliseu struck to put them 2-1 ahead on the night, and on aggregate.
However, Marco Reus drew Dortmund level in the first minute of injury time, before Felipe Santana scrambled home the winner from a seemingly offside position with just seconds to go, sparking wild celebrations among the hosts but furious protests from the visitors.
"They did not want us in the semi-finals," an enraged Pellegrini said of the match officials. "After it went 2-1 for us, there were so many refereeing mistakes.
"The third goal was a hammer blow for us. There were two dismissals, and there was also their offside in the act of making it 3-2.
"In the final 10 minutes, we were so impaired (by the officials). In such conditions, everything becomes very difficult."
Pellegrini admitted that Malaga will struggle to get over the nature of their European exit, but called on his players to finish their Liga campaign on a high.
"It is certainly not a bitterness that will go away from one day to the next," the Chilean coach lamented. "You can talk about a cruel defeat, but I do not agree, we have played a great game.
"Now we are looking to finish the championship as best we can."
Dortmund, for their part, now move on to the semi-finals, where they have already been joined by Real Madrid, who defeated Galatasaray 5-3 on aggregate.