The Argentine star struck three times, including two second-half penalties, to lead his side to a 4-3 Clasico win at Santiago Bernabeu.
With his first goal, which came just before halftime to level the contest at 2-2, Messi became the all-time leading goalscorer in Clasico matches, surpassing former Real striker Alfredo Di Stefano.
Martino admits he has run out of superlatives for Messi, telling reporters: "I can hardly talk about Leo but there's no need. It's compliment after compliment.
"Today he breaks another record. I hope he gives me the match ball!"
Karim Benzema's first-half double gave Real a 2-1 lead after Andres Iniesta's opener, only for Messi to level before halftime.
Cristiano Ronaldo's controversial penalty 10 minutes after the break put Real ahead once more, only for the game to turn on 63 minutes.
Sergio Ramos denied Neymar a clear goalscoring opportunity and was sent off, with Messi dispatching that spot kick and then another on 84 minutes.
Neymar was otherwise ineffective but Martino insists he produced the moment that mattered.
"Neymar's only 21 but it all happened with him. Ramos was sent off through his phenomenal diagonal run," Martino said.
Barca is a point behind La Liga leader Atletico Madrid (70 points), while Real is on the same number of points as its city rival, but behind based on its head-to-head record.
Martino, who claimed prior to the match this was his side's "last chance" of defending its title, admits his team is right back in the race.
"The league begins again," he said.
"But it doesn't change my perception that beyond El Clasico, it's just one game."
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