Barry, 30, put in the hard yards in the dramatic 1-0 victory over Manchester United on Saturday at Wembley.
Now the England international wants City to repeat that spirited performance on May 14 and end a 35-year wait for a major trophy.
Barry said: "The victory means so much and you could tell by the celebrations. But the players, in the back of our minds, know we've won nothing yet.
"The final is going to be as tough or even tougher. The pressure will be more on us, so we've got to learn from the United game and take that into the final."
Source: PA
Source: PA