The Three Lions claimed the bronze medal with a thrilling 6-4 victory over France in Saturday night's third-place play-off in Miami, securing England's best World Cup finish since lifting the trophy six decades ago.
Tuchel admitted, however, that the disappointment of missing out on the final and the chance to end the nation's long wait for another world title will continue to linger.
"You just said it yourself, it's the first medal in 60 years, the best World Cup on foreign soil. So, I hope the players can be proud of that. We are fiercely competitive and we almost don't allow ourselves to be proud of third place because 18 months ago we set the highest goal,” Tuchel said.
“We set the highest dream to chase and we were very, very ambitious with our dream to make it to the final and win the World Cup. So it's very, very painful if you miss out, the pain will stay for a while like I said yesterday but it will go away, the scar will stay. This is how it is in high level sport."
With the quick turnaround for the France match after losing to Argentina earlier in the week, Tuchel added that the win was even more emphatic.
"You cannot worship this performance, this mentality today is high enough. We had one day less to prepare, we have thousand kilometres more than our opponent in our bones and bodies,” the coach added.
“We come from altitude, we come from the heat over time. We came from playing with 10 men and again and again we found a way. Again, it was normal for us to show the mentality. There is a lot to be proud of but still a part of us will not be fully happy because we had the highest ambition and that's basically the situation."