Havertz struck on 97 minutes to earn the 1-0 win against Chelsea and send Arsenal into the Carabao Cup final 4-2 on aggregate.
Timber said afterwards: "The atmosphere at the end just makes me smile. On to Wembley! First of all, I didn't know if he (Kai Havertz) was going to pass. He went around the keeper and he did amazing.
"For Kai being out for so long and coming back and the love he gets from the fans says a lot. You could feel it coming, he goes around the goalkeeper, and you know everyone is going to go crazy.
"Chelsea are a great team. They have some amazing players. Bringing Palmer and Estevao on, they also have amazing players coming off the bench. When you win over two legs twice, I think you have done an amazing job, so credit to the team.
"The desire is there - we are very hungry. We are in an amazing position."