A 3-1 win over Milan at the Camp Nou on Wednesday saw the La Liga giants seal their place in the round of 16.
Lionel Messi scored a brace for Barcelona, including an 83rd-minute sealer, as they moved five points clear atop Group H.
Qualifying with two matches remaining delighted Martino but the coach still wants to finish top of the group.
"Qualifying on matchday four means the pressure is off but we still have an obligation to finish first in the group," Martino said.
"Because there are no real surprises in the groups you can assume that the favourites will get through but you never know who you will draw in the next round.
"We wanted to get out of the group early in order to feel better."
Martino was full of praise for Messi after the Argentine was criticised for going three matches without a goal ahead of Wednesday's clash.
But the Argentine coach was concerned about his team letting Milan back into the game when Gerard Pique diverted a cross from Kaka into his own net just before half-time.
"Making negative assertions about Leo has risks. He played phenomenally well today," Martino said.
"We allowed our opponents to get back into the game (before half-time), however, and that worries me."
