Jags lost 3-1 to the Gayfield side despite taking the lead in the first half through a Colin Hamilton own goal.
Michael McKenna levelled just before half-time and scored again early in the second period before Nicky Low added a third.
It was Thistle’s first Championship defeat of the season – and McCall says what matters now is how they respond this week at home to Morton.
He told the club website ptfc.co.uk: “During the first half we were as comfortable as I’ve seen coming to Arbroath with any team.
"We created some good opportunities, and should probably have had more than one goal to show for it.
“An individual mistake meant we weren’t leading going into half time which would have made all the difference. It’s a mistake and they happen but it needs to be learned from.
"We were punished for another individual mistake in the second half which meant the game was very stretched.
“It was a fantastic Thistle crowd that travelled up and we’re all disappointed that we didn’t send them home happy.
"Arbroath is never an easy place to go and we have no divine right to win, we have to earn it. In this league, you’ll lose games of football, but it is how you react to it that will dictate your season.
"We have to shake it off, train well and look forward to a game next week at Firhill where I’m sure the Thistle fans will be out in numbers making a terrific atmosphere.”