England's 5-0 win saw the nation qualify for next year's World Cup.
During the night, England's fans chanted towards Tuchel after he had complained about how quiet the support was during the friendly win against Wales at Wembley.
Tuchel said: "I got a bit of stick today in the first half, so fair enough. I take it in good humour, with a good sense of humour. I accept it.
"They had a reason today from my last comments and I guess that's fair enough.
"I got a bit of stick and I found it quite creative. It made me smile and this is how it has to be. It's British humour and I surely can take it. No harm done."
He added: "It's so important. They are here and I said the support in Serbia was brilliant. The support today was brilliant and we are very sure the support in America will be absolutely brilliant. We need it.
"It makes such a difference if you go out as a player or as a coach and you see the fans behind the team and singing. This is also part of what we do.
"We want to make them proud, we want to make them happy. They should be happy to watch us and they should be able to identify with how we play.
"We are on our way to build something and top performance from them today."