City were all but eliminated by Spanish giants Real Madrid during a 3-0 defeat in last week's first leg of a last-16 tie at the Bernabeu Stadium.
And the record 15-time European champions completed the job at City's Etihad Stadium on Tuesday with a 2-1 success for a 5-1 aggregate win after the hosts played most of that match a man down following captain Bernardo Silva's red card for handball.
Defeat capped a tough few days for City, with a draw at West Ham in between the two matches, with Real leaving them nine points adrift of Premier League leaders Arsenal.
They must now rouse themselves for an EFL Cup final against the Gunners at Wembley on Sunday, but City winger Doku is convinced team morale remains high.
"We played well (against Real)," he said. "We played well with 11 against 11 and 10 against 11. We created chances.
"I feel like if we play like that every game, we'll put many teams in trouble. There are some good things to take out of this game to the next one."
The 23-year-old Belgian winger added: "There's still a lot to play for. We're still in three competitions, three trophies to win.
"If we do that, it's still going to be a great season."
Turning to the League Cup final, Doku reckoned it was "a good cure" for City's European woes. "We'll do everything to win that game and to win a trophy," he said.
City started well on Tuesday, but were dealt a huge blow when captain skipper Silva was sent off after 20 minutes for handling a Vinicius Junior shot on the line.
Vinicius scored from the ensuing penalty and, although Erling Haaland equalised for City, defeat on the night was confirmed when Vinicius grabbed his second goal in stoppage time.
Doku insisted Silva had the full support of his City teammates.
"Obviously, he's disappointed," he said. "Knowing him, I know he takes it very personally.
"But even after it, we stood there, we were in the game. He's disappointed, but we're all there for him. We know his contribution to the team is massive.
"We can be proud of our performance. Playing against a big team like that, 10 against 11, and still performing like we did, still putting them into trouble. Not every team can do that."