The Gunners went down 2-1 to the Blues, but Parlour says Arsenal fans have plenty to be excited about.
"I've been impressed with Arsenal this season," Parlour, who scooped three Premier League titles during his time with the club, told Goals on Sunday.
"The new signings have come in and really settled in quickly - I really like Santi Cazorla, he looks like a top player - and they've had a good start.
"I know it was a poor result against Chelsea but they were looking good up until then.
"It's going to be a long season, of course. People are saying where can they come this year? Well Champions League football is the main thing for Arsenal football club. Can they bridge the gap between them and Chelsea, Manchester United and Manchester City? That's the level they've got to try to get to."
Parlour is also pleased to see his former team-mate Steve Bould brought in as Arsene Wenger's number two, succeeding the long-serving Pat Rice.
"I think Stevie Bould going into the management side of it has had a big impact for Arsenal as well," he said.
"Arsene Wenger has been a great manager for them and I loved Pat Rice when he was there but Stevie has brought something different to the team."
However, Arsenal - who haven't won a trophy since 2005 - are still a step behind the likes of Manchester City and Manchester United, says Parlour, and the former Gunner says it is hard for Arsene Wenger's side to compete against their big-spending rivals.
"A lot has happened at Arsenal football club since we were winning Premier Leagues," he added.
"Moving stadiums was a big thing for them. They had to do it because of the revenue coming in, but it was always going to affect them because of the resources they've got. I don't think they've had money to spend.
"Arsene Wenger's done a brilliant job and what he's achieved by spending hardly any money and what he's had out is amazing really.
"The contrast to when I was winning trophies with Arsenal was that it was only between Arsenal and Manchester United back then. If Arsenal didn't win it, Manchester United won it. Chelsea have got stronger and there are other teams, including Manchester City, getting stronger.
"I know Arsenal may have gone backwards a little bit because we're not winning trophies but the club itself has grown by moving to the Emirates. Globally it's getting bigger. But yes the fans are getting frustrated because the club was winning trophies.
"I was really disappointed in the Birmingham Carling Cup final. What an opportunity that was to win the League Cup and shut up a few people, but they missed out on that as well."
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.