Barca were eliminated from the competition thanks to a 1-0 quarter-final second-leg defeat at Atleti on Wednesday, marking the first time they had not reached the semi-finals since 2007.
Atleti and Real drew Chelsea and Bayern Munich respectively in the last four, and Martino feels the disappointment caps what has been a difficult year on and off the field.
"For me personally, getting knocked out was a failure and it will continue to be even if we win the league and cup double," he said. "I’d very happily swap places with either of Atletico or Real Madrid right now.
"It hasn’t been an easy year. There have been a lot of news stories. It hasn’t been a great year for the institution. So many ups and downs.
"But we never drifted off course or changed the way we play, we just played better or worse."
Barca are still in the hunt to retain their Liga title - and have the Copa del Rey final against Real on Wednesday - and sit one point adrift of leaders Atleti and two ahead of Real.
A trip to Granada on Saturday is next up for Martino's men, and the coach is wary of the hosts' battle against relegation.
"Granada need the points as much as we do. But we know what’s at stake," he added.
"We have to win every game we have left if we want to win the league."
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