The Gunners slumped to their second Premier League defeat of the season with a 1-0 loss to Sheffield United at Brammal Lane on Monday.
Arsenal have picked up 11 points out of a possible 30 in their last 10 Premier League games away from the Emirates stadium.
Additionally, they have kept just two clean sheets away from home since Unai Emery took over the club last season.
Arsenal failed to go 3rd on the Premier League table after Monday’s loss and the 46-year-old was gutted by the fact that the North Londoners could not win against the Blades.
“I thought it was always going to be a tricky game, I would have taken a draw,” Parlour said on the Alan Brazil Sports Breakfast.
“I mean, I had Arsenal to win the game…could have gone third. But, they’re still fifth and they’ve still got lots to play for.
According to the former Arsenal midfielder, anything less than a top-four finish this season would be a “failure” for the club.
“As I said before at the start of the season; if they come fourth, it’s a great season. Champions League football is the most important thing for Arsenal now going forward.”
“If they come fifth or sixth this year it has been a failure again. Because they went into the transfer market and I think everyone was quite excited about the signings.
“So I think it is going to be interesting to see what happens going forward.”
He added: “No, it’s not better (than when Wenger was in charge), but it is a real opportunity.
“After we started really well during the start of the season, people were going ‘Oh we can challenge for the title’ and I said no chance.”
“I said that on here – no chance whatsoever. If they come fourth in the league, it’s been a very good season.”
“They’re fifth at the moment and still have every chance of coming fourth so it was a poor result the other day.”
“But the other teams are struggling as well around them that might give them an opportunity to get fourth place, which would be a great season for Arsenal.”
Arsenal will be looking to continue their 100 percent start to the group stages of the Europa League with a win against Vitoria SC on Thursday night.
