They face holders Wigan in the first semi-final at Wembley on Saturday, knowing a win will see them play either Hull or Sheffield United in the final on May 17.
Parlour, who lifted the FA Cup four times and was a runner-up once, believes winning the tournament is now more important for Arsenal than qualifying for the Champions League.
"For me it's all about winning trophies," said Parlour, speaking on behalf of official FA Cup supporter williamhill.com.
"I know the Champions League is important as well but if someone asks you at the end of your career what you've achieved and all you've got is coming fourth eight years running - what is that?
"It's great for the club financially but you don't want to be a professional footballer to make money for your club - the whole objective of being a footballer is to win.
"I was lucky to win lots of trophies when I played and for the history of the club it's all about silverware.
"It would give the club a big boost for next season because all those players are good players but they need to win something together.
"That's the big thing for me - fourth and a trophy would be fantastic but if I had to pick fourth and no trophy or fifth and a trophy, I would definitely take the trophy."
Arsenal's drought has placed added scrutiny on the future of Wenger, who is yet to sign a new contract with the club.
Wenger has delivered Champions League qualification in every one of the 16 seasons he has been at the helm but that record is in danger of ending after a 3-0 loss to Everton last weekend.
Roberto Martinez's side are now only a point behind Arsenal in the league table, with a game in hand.
Parlour admits the pressure on Wenger will be enormous if Arsenal fail to lift the FA Cup but the two-time double winner believes fans should be careful what they wish for.
"The pressure on Arsene would be huge if they don't win the FA Cup, there's no doubt about that," Parlour said.
"You look at how some of the Arsenal fans react at the Emirates, they're fed up with how the team are playing.
"But changing a manager, it's not easy, you've got to have a plan.
"There are other good managers around the world, but a lot of them are in good jobs and would they leave their job to come to Arsenal?
"They have to know the next guy could do as well if not better than Wenger and the grass is not always greener."
Arsenal have won the FA Cup 10 times - twice as many as Wigan, Hull and Sheffield United put together - and can equal Manchester United's record of 11 this season.
Wigan, currently fifth in the Championship, are the holders after pulling off a shock win over Manchester City in last year's final but it is Wenger's side who are strong favourites.
"Wigan are going to play with no pressure whatsoever," Parlour said.
"Their main objective this season is to get back into the Premier League and after last year, they know Wembley very well and so do the supporters.
"All the pressure is on Arsenal but that's when you've got to step up, that's why you're a top player, that's why you play in big teams - to handle pressure."
Parlour added: "You can't get a bigger occasion than playing at Wembley in a semi-final in front of a full house.
"It's a big opportunity for Arsenal to show they can bounce back - it's about their mentality and passion going into the game.
"The league is no longer in their hands but the FA Cup is and it's vital."
:: williamhill.com are an Official Supporter of the FA Cup
Latest odds: 2/5 Arsenal, 7/2 Draw, 7/1 Wigan
Source : PA
Source: PA