Tuchel will become England's third overseas head coach for the men's team when he starts work on January 1, raising questions over the strength and depth of top-level English coaches.
Tuchel, who has been out of work since leaving Bayern Munich at the end of last season, hopes to win hearts and minds, as well as the World Cup.
The 51-year-old's appointment is on an 18-month contract through to the 2026 FIFA World Cup.
FA boss Bullingham said there were English candidates among the "approximately 10" people interviewed for the job, but former England defender Gary Neville claimed the decision to go for a foreign coach was a "big blow" to domestic managers.
The job profile published by the FA on July 19 - three days after Gareth Southgate's exit - said the governing body was looking for someone with "a strong track record delivering results in the Premier League and/or leading international competitions". No English boss has won the Premier League, and the last Englishman to win the European Cup was Joe Fagan back in 1984.
Bullingham sought to give his backing to the work being done to develop homegrown talent at the national football centre at St George's Park, which he said had been "a really good success".
"There are a lot of fantastic young coaches around and obviously (Tuchel's assistant) Anthony (Barry) is one of those," Bullingham said.
"Any federation in the world that is looking to hire a senior manager, clearly you would love to have five to 10 domestic candidates who are coaching clubs in your domestic league, challenging and winning honours in your domestic league and European football.
"We are not quite in that place at the moment.
"We would love to have more English coaches managing in the Premier League, for example."
England's anthem was among the many topics covered off in Thomas Tuchel's first press conference. (AP PHOTO)
Tuchel and Bullingham defended his January start date, with the former saying he wanted to "have a clean start and a bit of time to recharge fully".
Tuchel's first press conference included an apology to the sceptics about his German passport, as well as a pledge to make a decision before his first game in March about whether or not to sing the national anthem.
"I'm sorry, I have a German passport," he said at Wembley.
"Everyone has their opinion and I can understand when someone says 'I would fancy an English coach for an English team'."
Tuchel's stint at Chelsea included arguably his greatest achievement as coach, winning the 2021 Champions League title.
He will be based in England, with occasional trips home to visit his family in Germany, and is itching to throw himself back into everything his new adopted country has to offer.
"It's the humour, it's the way of life," he said when asked why he liked English football so much.
"It's the attitude from the supporters to the game and what they demand from the players. It shapes the character of the players."
