Arsene Wenger's side slipped to a 2-1 reverse against Dinamo Zagreb, with Theo Walcott netting a late consolation after Junior Fernandes had added to Alex Oxlade-Chamberlain's own goal.
Olivier Giroud was sent off in the first half on a disappoitning evening for the Gunners, and it wasn't until Coquelin's introduction after the hour mark that the visitors began to get a foothold in the game.
Parlour feels that the tenacious Frenchman offers something different to the rest of his midfield teammates, and the 'Romford Pele' claimed that Coquelin was sorely missed in the opening 64 minutes in Zagreb.
Parlour told Sky Sports News on Thursday's Morning View: “I think you should always you should play your best team and [Wenger] did shuffle the pack and make the changes to try and keep everyone happy.
“For me, the man they missed most was Francis Coquelin in midfield. For me, he’s the man in midfield who makes the tackles and wins the ball, and they got overrun sometimes in midfield.
"When he came on there was a big change in how they played, so he was a big loss.
“Defensively they know they need to be solid and hit them on the break, so it was a disappointing night and performance. On the night, the sending off didn’t help and they are up against it."
Wenger's decision to pair Mikel Arteta alongside Santi Cazorla left the Gunners looking lightweight in midfield, and the side were overrun in the engine room prior to Coquelin's appearance from the bench.
A big criticism of Wenger over the years has been his steadfast refusal to add a defensive-minded midfielder to his squad, but Coquelin's emergence last season has cooled talk of the need to sign a specialist holding player.