The Argentine star struck three times, including two second-half penalties, to lead his side to a 4-3 El Clasico win at the Santiago Bernabeu.
With his first goal, which came just before half-time to level the contest at 2-2, Messi became the all-time leading goalscorer in El Clasico matches, surpassing former Real striker Alfredo di Stefano.
Martino said he had run out of superlatives for Messi but is hoping for a different gift from the 26-year-old.
"I can hardly talk about Leo but there's no need. It's compliment after compliment," Martino told reporters.
"Today he breaks another record. I hope he gives me the match ball."
Karim Benzema's first-half brace gave Real a 2-1 lead after Andres Iniesta's opener, only for Messi to level before half-time.
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 another on 84 minutes.
Neymar was otherwise ineffective but Martino said he produced the moment that mattered.
"Neymar's only 21 but it all happened with him. We were level through and Ramos was sent off through his phenomenal diagonal run," Martino said.
Barca are a point behind La Liga leaders Atletico Madrid (70 points), while Real are on the same number of points as their city rivals but behind based on their head-to-head record.
Martino said his team were right back in the title race.
"The league begins again," he said.
"But it doesn't change my perception that beyond El Clasico, it's just one game."
