Everton's below-par domestic campaign has left them 17 points adrift of the Premier League's top six and so the Champions League qualifying-round place on offer for lifting the Europa League offers a potential route to European football next season.
"Realistically the best hope we have is to go on and win this competition," said Barry. "It's a massive target for us.
"We have already showed we are more than capable against the best in Europe to win games. We know on our day we can beat anybody."