Barcelona gave away 4-1 lead in the reversed fixture in Camp Nou and were thrashed 3-0 in Rome on Tuesday.
Messi was not enabled to lift his side from slumping as they crashed out on away goal rule.
Spanish outlet Don Balon reports that Real Madrid’s Ronaldo blamed the defeat on Messi.
Messi started the season in fine form and still has 39 goals to his name so far.
Ronaldo, however, was dreadful at the beginning of the campaign but has since managed to overtake Messi on 40 strikes for the season.
The report said that the Real Madrid star thinks Messi is now saving himself for the World Cup in June.