"The top four is going to be really tough," Barry told the Liverpool Echo. "If we are going to set a target, then the top six is more realistic.
"The players are aware the fans are frustrated but it is down to us to play through that."
For Barry, Wednesday's game offers a chance to bring back the feel-good factor and breathe some life into Everton's faltering campaign.
"We have big games coming up in cup competitions. We focus on a huge game against Man City and hopefully we can get the fans positive again and then return to the league," he said.
"In an ideal world, going into a game like Wednesday would be with a win.
"There is nothing better than going into games on a winning run, when you are feeling confident, but that's where we are at the moment. We have got to go into a League Cup semi-final on the back of a defeat."
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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