Arsenal came from behind to beat Chelsea 2-1 and make it three wins from three in the Premier League this season.
Martin Odegaard found the winning goal in the end, much to the delight of the Emirates Stadium where belief is rising that the Gunners can defend their Premier League title.
Chelsea stunned the home fans by taking a second-minute lead through Morgan Rogers but threw the advantage away before half time.
However, after forging a comeback in the second half, Chelsea could have snatched a point on multiple occasions, with Estevao coming closest with a fine shot that goalkeeper David Raya tipped over the bar.
Speaking to the club website, Lacroix revealed that Chelsea may have deserved more but will learn from their mistakes.
“We are a little bit unhappy, of course, after losing, but I believe that we did well to be honest.
“We just have to adjust some points. I think it’s not easy to play there but we did good.
“We accept the loss but we want to learn from it. I think it’s good to learn about the mistakes and all the wrong parts. We have to go forward and go again.
“I think it was a good start but once they scored it got more and more difficult. But we showed that we also had good actions and good attacks, so the defeat hurts a little bit. We gave our best.
“I think we deserved more. Luck was not by our side, but we have to accept it. The desire to score, the attitude was clear. We showed good character until the very end. We deserved the 2-2, but we learned for next time.”
Chelsea finished in 10th place, a whopping 33 points behind Arsenal last season and they currently sit 4th, 3 points behind the Gunners.