The Citizens won their fourth successive league title, beating Arsenal by two points after winning against West Ham on the final day.
After their final day win over Everton, Havertz told TNT Sports: "What can I say? I feel sorry for all the Arsenal fans. We gave our best but it wasn't enough.
"Maybe in two or three months we can say it was a good fight. Right now I feel like we deserve more. It wasn't enough in the end but we go again next year.
"We showed great character again, they didn't make it easy for us. They took time with every throw and every ball. In my opinion it's sometimes not fair in football but we have to accept that football is hard. Hopefully we can go again next year and give Arsenal fans what they need and what they're all here for."
On his message to the fans, he added: "Right now I can't even think. It's just so frustrating. It's tough. I can tell them next year that we're going to be an even better team and we're going to give everything again. That's all I can say."