Fede Valverde struck for the 1-0 win three minutes into injury-time against Athletic.
Ancelotti said afterwards: “Valverde was key. He scored the winning goal. The team did well. We were slower in the first half, but in the second we did very well in every aspect. We wanted to win and react after getting knocked out and the team delivered.
“In the first half, we had good control because we had more players in midfield. We didn't suffer the pressure that we usually get from Athletic Club.
"We didn't create chances because we were missing players between the lines, which we added in the second half. In the first half, we were aggressive and recovered quickly.
"The team was more solid and united, and we didn't concede a goal. That's good news, and let's see if we can continue to improve."
Vinicius Jr always shows right attitude
He added, “I picked a line-up to have more control with (Luka) Modrić and (Dani) Ceballos, who played well for 60 minutes after a long injury. Then, to try and score, I brought on Endrick and more players up front. We have another game on Wednesday and this win is good for us because it gives us a boost."
On Vinicius Jr's performance, Ancelotti insists he was pleased.
"He's an extraordinary player with a fantastic attitude. He tried hard and in the second half he wore down the Athletic Club full-back. He scored a goal and made two or three very good passes. He was decisive.
"These haven't been happy days for him or for us. I really liked his reaction on the pitch and he's going to be a very important player in the coming games. I have no doubt about that. He's a very important player for us because of what he does on the pitch and his attitude."