Everton have been guilty of conceding far too many goals so far this season.
The Toffees were beaten 4-3 by Stoke City in their latest outing, as their defensive issues were exposed yet again.
Everton have tried to play on the front foot throughout matches this season, but Barry believes this approach is harming the team.
“We need to change our mentality and as a team being able to realise the situation of the game," the central midfielder said.
"We have got attacking players that do want to score goals but once you get ahead in an end-to-end game like that there is an opportunity to win, which is the third goal for us, and we need to close the game out. We have to change our mentality that we don’t need to score again but need to keep a clean sheet to win the game.”
Barry’s public comments come just days after the Daily Mail have suggested that Everton’s senior players have voiced their concerns to Roberto Martinez.
According to the Mail, a number of Everton’s experience players have urged Martinez to start deploying a tactic which offers their defence greater protection.
The Spanish boss is said to be determined to keep playing with an expansive style, though, as he feels his side can still push for a European place.
Everton are only four points away from the top six, meaning there is still reason for optimism about their chances in the second half of the campaign.