The former Arsenal midfielder was livid with the north London side's performance after they lost 3-1 - at home - to the Ligue 1 outfit.
It isn't the first time Arsene Wenger's side have suffered an embarrassing collapse in Europe and, should the Frenchman stay at the Emirates Stadium in the long term, it most certainly doesn't look like it'll be the last.
Another common theme to Arsenal's Champions League failures, meanwhile, seems to be a lack of impact from their big-name players.
"The big players like Ozil, Sanchez and Welbeck didn't turn up. We needed them to dictate the game but they were not in the game at all," he told Sky Sports News.
Meanwhile, the former Gunner could also not ignore the gaping deficiencies in Arsenal's back line, with Per Mertesacker in particular looking lost against Monaco.
According to Parlour, the German lacked desire, more or less inviting his man to have a go at goal and put the Gunners out of their misery.
"I didn't see a desire from Mertesacker to get across," he added.
"Centre-halves like Tony Adams and Sol Campbell would have had the desire just to make sure they got something on that ball but it looked like he said, 'have a shot, if you hit it in that far corner you'll probably score a goal'."
Arsenal return to Premier League action this weekend against Everton on Sunday afternoon. But what good is finishing fourth every year if the north London side are to lose at the first opportunity in Europe the following campaign?
It's a question Arsenal fans are no doubt used to hearing...