Messi himself scored a stunning free-kick in the contest, but it was one of just two shots on target in 90 minutes for the Catalan giants, who have toiled for form in much of their outings post-restart.
The Argentine is known for being protective and reserved with his views but after giving up the title he spoke to Movistar+ and gave one of his frankest assessments as to where this current Barca are currently at.
He said: "We didn't want to finish like that but it is a mark of how the season has been: an inconsistent and very weak team. Other teams beat us in intensity and determination.
"If we're not good enough for La Liga, how will be good enough for the Champions League? Roma, Liverpool... the fans are losing patience because we're not giving them anything. If we want to fight for the Champions League, we have to change many things. We need to be self-critical."
Messi's demand for reflection comes at the end of a dreadful 2020 for the club, in which all manner of things have gone wrong, leading to speculation that Messi was interested in a move away from the club.
He added that he had warned of what was to come, saying: "I already said that if we carried on as we were, it wouldn't be good enough in Europe. If we want to fight for the Champions League, we are going to need to change a lot."
"Madrid did what they had to do. Not losing since the break has a lot of merit. We need to be self-critical, starting with the players. We are Barca and we are obliged to win all our games."