Los Blancos sealed their spot in the semi-finals after their 4-2 win in extra time at home to Bayern, coming out on top 6-3 on aggregate.
Referee's Viktor Kassai's performance was widely criticised after he controversially showed Arturo Vidal a second yellow card for what appeared to be a fair challenge late in the match before allowing two offside goals in extra time.
Former Colombia international Asprilla - who played for Newcastle United and Parma - didn't hold back, suggesting the Bundesliga champions were robbed.
"No more robberies for Real Madrid, they are a team of rats."
Asprilla joined fellow critics in Bayern boss Carlo Ancelotti, Vidal and Arjen Robben in claiming the match was unfairly officiated.