Lionel Messi's 27th-minute opener was cancelled out late on by Antoine Griezmann as Barca were held to a 1-1 draw by Real Sociedad on Wednesday.
But the draw was enough after Barca's 2-0 win in the first leg and Martino said it was important to reach the decider, where they will face Real Madrid.
"There are three objectives this season and we fulfilled one of them today," he said.
"We completed our objective. These players always play in finals."
Messi collected a sloppy pass on the halfway line before going alone and opening the scoring despite Enaut Zubikarai getting a hand on the effort.
Griezmann's good finish from Gonzalo Castro's cutback in the 87th minute was far too late for Sociedad.
Martino said there was plenty of improvement to come from his side, who are top of La Liga.
"We can improve, we still have a lot of time," he said.
"(We played) a good match, but we can still play better, we still have time to improve – we can do it for more than 50 or 70 minutes. We could have scored more goals.
"We had the obligation to qualify, we couldn't miss it."
