Arsenal won 2-0 thanks to goals from Declan Rice and Viktor Gyokeres.
Parker said: “We started well but then their class shone through after their first goal.
“We knew their set-piece threat and it showed again today. They’ve got a mentality about them when they get a set-piece and they took their chance well.
“We looked a bit stunned after that goal but in the second half, I can’t fault us at all. It was a second half performance to be proud of.
“We showed real impetus in that second half. We gave them a really good game but just fell a little bit short."
Parker also stated: “These games won’t define us but I saw enough to encourage me again today.
“We were competitive and caused them problems in that second half. I thought we had an edge and a confidence about us.
“Of course there’s elements that you can always improve on, but we’ve come up against a very good side today.
“This team are going in the right direction. I’m sure of that. There were large elements I liked and after ten games of the season, I’ve said that in every game, so we’re moving in a positive way.
“I’m satisfied with the performance and the start we’ve made to the season. We’ll keep preparing right, keep doing the right things and focus on the next one at West Ham next weekend."