Tuchel told reporters he had not heard the booing, which contrasted to applause for Croatia's veteran forward Luka Modric as he left the pitch and was widely reported by media present.
The Arsenal player was making his first appearance for England since March, before the World Cup which he was not selected for due to injury, and has been booed in the past after turning his back on the national team.
He left the 2022 World Cup camp in Qatar early for personal reasons and later made himself unavailable for the remainder of Gareth Southgate’s tenure as England manager, which ended after EURO 2024.
"I didn't hear the boos for Ben and I thought we were past that chapter," said Tuchel after a match that saw captain Harry Kane celebrate his record 126th cap for England with a match-winner from the penalty spot.
"I hope it doesn't happen again. He's a player of us. Since I'm in charge he's desperate to come and be with the group. He doesn't put a foot wrong since I'm in charge.
"I can only judge him on what I see and what I experienced and it is on the highest level and he can really help us to win football matches," added the German. "Like I said, he's part of our group and we will protect our group. He deserves to be with us."
Tuchel said he was not worried White might turn his back on the team if the negative reaction continued.
"I don't think so. I don't want to make it bigger than it is," he said. "He seemed to me always committed and always dedicated and excited to come into camp and get a call-up... there is no reason to doubt his commitment or his passion.
"He overcame the boos the last time, I didn't hear them this time."
