51-year-old former Chelsea and Bayern Munich manager Tuchel has made history as the first German to lead England, following in the footsteps of only two other foreign managers - Sweden's Sven-Goran Eriksson and Italy's Fabio Capello.
Newcastle United's Eddie Howe, one of only three English managers in the Premier League, and former Chelsea head coach Graham Potter were among those linked with the job before the FA named Tuchel as Gareth Southgate's successor on Wednesday.
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"They probably got the best available coach in the world at this moment in time," former Manchester United captain Neville told News. "Fitting that criteria they are absolutely spot on.
"I am not sure it meets the criteria of St George's Park and the belief in English coaches and the growth in the English teams' performances over the last few years.
"Everybody in our country including myself will wish him all the best and hope we can get over the line and win a trophy, but I think there are some serious questions for the FA to answer in respect of English coaching.
"I do think we are damaging ourselves accepting Tuchel is better than any of the other English coaches."
Tuchel, who will be assisted by English coach Anthony Barry, will begin the role in January ahead of England's qualification campaign for the 2026 World Cup.
England reached the final of the European Championship in 2020 and 2024, as well as the World Cup semi-finals in 2018, under Southgate but are still without a major trophy since the 1966 World Cup.
"I'm not the most patriotic of people, the England manager has to be this or that — it's not about England," former Liverpool defender Jamie Carragher told Sky. "It's international football. The whole point of it, certainly with the major nations who compete for titles, is it's our best versus their best."
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