"It's been a wake-up call for everyone," the 24-year-old Coquelin told the club website.
"Considering the recent results we had before that, going really well in pre-season, it's disappointing and it was not an Arsenal performance."
However, Coquelin was confident the FA Cup winners could respond immediately when they travel south to Selhurst Park for Sunday's fixture against Crystal Palace, who won 3-1 away at newly-promoted Norwich City last week.
"In bad things, good things can come out too. It’s good that it happened in the first game so that now we can pull ourselves together with 37 games left," Coquelin said.
"We know the quality we have and we need to respond straight away. We've been working really hard in training and we need to put all of the training effort into the game."
Coquelin, who was loaned out to three different clubs before enjoying a breakthrough season last year, said the team knew they had to put in more.
The defensive midfielder said title rivals Manchester City had set the bar over the opening round of matches with their 3-0 win at West Bromwich Albion.
"When you look at different teams I think a lot of them are ready," the former France under-21 international said.
"You look at Manchester City when they played against West Brom, I think they played really good football."
(Reporting by Shravanth Vijayakumar in Bengaluru. Editing by Patrick Johnston)
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