Messi's long-standing rivalry with Real comes from the 21 years he spent with their arch-rivals Barcelona.
His current team, Paris Saint-Germain, were knocked out by Carlo Ancelotti's Los Blancos in the quarter-final stage, a tie in which PSG dominated much of.
The Spaniards did a similar thing against Chelsea and Man City in the following rounds, before beating Liverpool by a single goal in the final, despite having just four shots to the Reds' 24.
And Messi insists that Madrid were not the best team in the competition this season, before stating that he is taking nothing away from their 14th European Cup win.
"The Real Madrid game killed us - the best team doesn't always win," Messi told Argentinian broadcaster TYC.
"Without taking anything away from Madrid, because they are the champions of Europe and they're always there or thereabouts, but they weren't the best team of this Champions League.
"The Champions League is about situations, key moments, psychological moments that take a team, where the slightest error can eliminate you and those who are best prepared for those situations end up winning or reaching the final."
After over two decades at Barcelona, Messi was forced to leave last summer after the club were told they could not afford his wages due to LaLiga limits.
As well as their earlier than expected exit from the Champions League, the superstar endured a difficult time in the French capital this season, which led to him and his teammates being jeered by home supporters.
And it was something that Messi has labelled as 'tough' and 'difficult', which could hint at his desire to return to Barcelona in the near future.
"It was a summer of complete happiness and one where I thought everything would stay the same at Barcelona and in my life, and then what happened happened and it was tough," he added.
"It was a tough change, a difficult year. The adaptation wasn't easy. After a lifetime in the same place, it's not easy at my age.
"It's one thing to do it when you're younger and you want to, but at the time I didn't want to and I didn't imagine or expect it."
"It's also new for me. It's a different situation. It had never happened to me in Barcelona, quite the opposite," he went on to say when asked about the boos from PSG fans.
"The anger is understandable. Then if I agree or not about the whistles to me and to [Neymar] in particular, that we were the most marked. But well, it happened.
"I did not like that my family was there and that they heard people whistling at me, and that my children were there."