Everton are currently in the semi-final of the FA Cup.
Everton’s failure to make a challenge for a Champions League place has frustrated their supporters, but Barry still feels that the season could be a productive one.
Everton remain in the FA Cup semi-final, and Barry insists that winning the cup would be a more exciting prospect that breaking into Europe’s top competition.
“You play the game to win things and if you asked me whether I would want to finish in the top four or win the FA Cup, it'd be FA Cup every time,” he said.
Everton’s poor league form has led to Roberto Martinez falling under serious pressure at Goodison Park.
The calls for the Spaniard to be sacked are growing louder by the game, but Barry insists that he is still behind the former Wigan Athletic boss.
“He's a very good manager and been very good for me,” the former England international said. “He can quiz us on what we've seen. I've never met a manager as passionate or knowledgeable about football.
“Confidence and momentum are huge in sport. Having said that we have everything to play for, this could still be one of Everton's best seasons in recent years. We are two games away from winning a major trophy and we have to believe we can do that.”
Everton now face a season-defining week, and one which could be crucial to Martinez’s future.
The Toffees first take on Liverpool in the Merseyside derby at Goodison Park later this evening, before taking on Manchester United at Wembley in the FA Cup at the weekend.