The Argentine scored a hat-trick in the Bernabeu as he became the all-time leading scorer in Clasicos, but the 26-year-old has lavished praise on the entire team.
"On a personal level things are going very well for me but I have to point out that the whole team had an extraordinary game," Messi told reporters.
"This team always rises to the big occasions. We like playing in these types of games.
"We have to keep going. The league is very tough and we haven't got many games left. We can't afford to fail.
"It's an important win. We're back in the race again and we have to keep going. We can't make any more mistakes."
Messi has now scored back-to-back hat-tricks in La Liga after also netting a treble against Osasuna last weekend.