The 50-year-old joined the Spanish champions in the close-season, replacing Tito Vilanova, who resigned following a recurrence of throat cancer.
Martino has seen his side make a bright start to the season, winning all four La Liga fixtures, as they sit first in the table.
His charges now begin their quest to win the Champions League for the first time since 2011, and they will hope to improve on last season's disappointing 7-0 aggregate defeat to Bayern Munich in the semi-finals.
"For every coach taking part in the Champions League is a very important part of their career," Martino said ahead of the side's opening Group A fixture with Ajax at Camp Nou on Wednesday.
"Of course I'm looking forward to it. And when you're able to do this with a great squad, it relaxes you. And Barcelona has a great squad."
Despite their winning start to the new campaign, the Catalan giants have received some criticism for their performances.
They needed an injury-time winner from Alexis Sanchez to defeat Sevilla 3-2 on Saturday after initially surrendering a two-goal lead, and Martino knows his side can improve.
"We've been speaking about what happened especially over the last couple of games, and in terms of the opponent," he said.
"What I ask is that they make the right choices in the right moment. Sometimes you can play the ball about more. We're gradually improving in these areas."
Brazilian forward Neymar could also make his Champions League bow on Wednesday, following his move from Santos.
And Martino has backed the 20-year-old to be ready for the challenge.
"In the case of Neymar, it is his first Champions League game," he continued. "But this is one game in a long list of games in his career.
"He's very young and has plenty left in his career. Just like me, the players are looking forward to this competition.
"He offers us a lot of options around the pitch, not only in terms in of attack, but also holding up the ball and defending."
