Harry Kane, Marc Guehi, Noni Madueke, Ezri Konsa and Marcus Rashford's penalty were the goalscorers on the night.
A buoyant Tuchel declared afterwards: "I told you! Yes, you need a bit of trust in what we're doing. We tell you what we feel, and we see what we see in camp – I don't lie to you. If I didn't see it I would say we're not there yet.
"I am glad the players could show what they showed me during this week. This week was excellent. The attitude, the way we played in both matches. Today is a statement victory against a difficult opponent in a difficult environment. I think it was the teamwork, the team performance – we helped each other out.
"And there was no negative attitude on the pitch, no frustration on the pitch. For me, it was teamwork in it's purest form. Then we played football to a high level and got a deserved win."
On the added pressure after a strong victory, the German added: "Of course, I understand that, but it is normal. It is our job to keep this going. Players go now to their clubs, but I am very sure that everyone - staff and players feel what this means.
"This camp was the benchmark."