The England midfielder believes if the Blues are to win the trophy, they will have to beat either United or Chelsea at some stage anyway.
With a replay needed to decide who the semi-final opposition will be, Barry claims he has no preference for who the opposition will eventually be.
“I don’t think the lads are too worried about it,” he said. “We were always probably going to have to beat United or Chelsea at some stage to win it anyway.
“We beat Chelsea not that long ago and, of course, beat United in the semi-final two years ago at Wembley so that could be in the back of their minds if they face us again.
Winning that game was I think that was a massive step for us - to beat United and go on and lift a first trophy in 35 years was crucial to our development as a team
...Gareth Barry...
“It gave us the confidence and belief to go into that next season on a high so that was a big turning point for us.”
Barry has rarely missed a game since joining from Aston Villa almost three years ago. He has clocked up 167 appearances for City so far and admits he is keen to continue playing for the Blues beyond his current deal.
“I’ve got the rest of this season and then one more year as things stand,” he said. “Everyone is pretty relaxed because there have obviously been changes over the past year.
“It just important we keep performing on the pitch and hopefully everything will fall into place. I want to finish my career still challenging for trophies and this is the perfect club to do that with.
“I’m very settled here but at the same time I have got a lot of respect for the people who have come in and they are going to have a good long look at the way they want to go and the players they want to go with it so as individuals we need to work hard when we get the chance.
We’re still desperate to retain the title and we are not going to write that off despite United’s points total. They keep winning and you’ve got to hold your hands up and say they have had a fantastic season
...Gareth Barry...
“But I think winning the FA Cup would go a long way to saying it has still been a good season for us.
“The lads have shown great character to bounce back from the Southampton set-back with four wins on the bounce, scoring 12 goals and not conceding any.
“It is important that we finish strongly, keep the cup run going and try to win it, while trying to get as close to United as possible.”