The Catalan outfit were knocked out of the Champions League quarter-finals by Atletico Madrid earlier this month, before losing the final of the Copa del Rey to Real Madrid.
Martino's side are also four points off the pace in La Liga, but Pique has thrown his support behind the under-fire Argentine.
"There are no excuses, we haven't performed as well as desired and we're the first to take the blame. But we all have to look at ourselves," Pique told reporters.
"I think that Martino is not to blame at all for what has happened this season. He came in at the last minute and he has worked hard.
"We're Barca and we'll always be fighting fit. It hasn't been our best season, but we'll pick ourselves up. The future is exciting and we'll make it a success. I trust the people who run the club, we have a great squad."
Pique is currently on the sidelines with a pelvic injury.