The England international believes that his teammate's new contract will send out a strong signal of the club's intent and will help to attract further talent.
The Ivorian midfielder recently signed a deal that will keep him at City until 2017, and Barry was delighted to see the 28-year-old extend his stay at the club.
"When a player like him gets a new deal, it is a lift for everyone," Barry told reporters. "You don't want to see players like that leaving. You want others like him coming in.
"When you can keep players like him for another four years, I am sure there will be others coming in, of the same level, to join him."
Roberto Mancini's men travel to Wembley on Sunday for their FA Cup semifinal against Chelsea, and Barry is convinced that whoever triumphs in that game will go on to lift the trophy against either Wigan or Millwall.
"It feels more like a final," Barry said. "This is the bigger game of the two and if we can get through it this could be another FA Cup for us.
"I am looking forward to it. You want to be playing big games at this stage of the season, as this is, when they hand out the trophies."
City go into the game on the back of victory over rival Manchester United at Old Trafford, and Barry says while his side was thrilled with the win, there were still some regrets after the match.
"To win at Old Trafford two years in a row sets a good standard for our club," Barry said. "The players were desperate to get three points and we would have been disappointed to get anything else, even a draw.
"To win for a second year running is a fantastic feeling, but there is some frustration that we haven't played like that more often.
"Even before the game kicked off, our players were thinking that we wished there was a little bit more at stake and the gap was a little bit closer."