Brian Cipenga had fired the Congolese into a shock lead after seven minutes in Atlanta, but Harry Kane scored twice in the second half of a nervy contest to send England into a last-16 meeting with tournament co-hosts Mexico in the Estadio Azteca.
"We kept believing. We had the worst start possible. First shot, first goal, Then, it became even more difficult," said Tuchel.
Kane was denied a first-half penalty after it appeared DR Congo goalkeeper Lionel Mpasi had tripped him.
"After the first water break, we were on top of the game. I think we should have had a penalty," Tuchel added.
"The substitutes came on, and put the effort in, and we won it. Well deserved, but we had to work a lot.
"We have to have that mindset if it is getting hard, it is getting hard, but don't lose patience and don't lose belief."
Of Kane, Tuchel said admiringly: "He is getting better."