The Brazil international became the first player to score a three-goal haul in both the Copa Libertadores and the Champions League as he struck three times in 14 minutes during a sparkling display.
Neymar has now found the net eight times in all competitions since joining Barca from Santos in June and Martino was quick to hail the 21-year-old for his contribution to an excellent performance from the Catalan club on Wednesday.
"Neymar didn't start well, he had to adapt to the centre-forward position, but after the first goal he showed what he can do," the Barca coach told reporters.
"What amazes me most about Neymar is how he's involved with the team, how he helps to recover balls - that's rare for such a player."
Martino also suggested that Barca delivered their most complete showing of the campaign against Celtic and is hopeful that his side can continue to perform at the same level.
"I think this was our most complete game this season," he added. "I'm especially happy that we could keep up the level for a long time.
"Our goal is to play every game like we played tonight."
Barca are back in action on Saturday in La Liga against Villarreal.