The 26-year-old's treble at the Bernabeu moved him clear of former Madrid striker Alfredo di Stefano as the all-time leading scorer in Clasicos.
"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," Martino told reporters.
Next up for Barcelona is a home clash with Celta Vigo on Wednesday evening.