Daniel James was shown a straight red card for a dangerous high tackle on Kovacic, who was forced off with an ankle injury.
Tuchel said, "If we did not have the major injury to Mateo Kovacic, it would have been close to a perfect evening. It was a very strong performance from the start.
"We accepted all the obstacles we'd have to face - a physical team and an emotional stadium. We were strong from the beginning and deserved to win.
"We never dropped in concentration. We stayed very disciplined to avoid any chance of offensive transition. We did what we had to do at a very high level."
On Kovacic's injury, he said: "It looks swollen and painful. It's the same ankle he had injured already. It doesn't look good."
"We were very focused. Even against 11 players we were clearly the better team. I felt the team were very commited, focused and calm. I had a good feeling.
"I was happy with how we played and how the players reacted after Saturday's late equaliser. We trusted ourselves but it was necessary to clear the air and refocus.
"The level of discipline and coverage in the defensive approach, we were more careful than the last game. We took care that we have a clean sheet."
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