The Spain international was not impressed with his side's finishing in the first half, but was pleased that the Blancos eventually secured second spot in their section
The Liga champions missed numerous chances to double their 1-0 lead before half-time, and saw City restore parity after the interval as Sergio Aguero converted a penalty, much to the disappointment of the Madrid goalkeeper.
"We had chances to finish the match off before the break, but Manchester City made things difficult in the second half," Casillas was quoted as saying on the official Uefa website.
"We had a tough time after [Alvaro] Arbeloa's sending-off, and they got some momentum from that, the penalty and the equaliser.
"We struggled but we managed to get what we needed from the match and to qualify.
"I agree with [Jose] Mourinho. The important thing was that we got through to the round of 16, we had a very tough group."
Madrid sit second in Group D with eight points from five games, four points ahead of third-placed Ajax, while Borussia Dortmund top the table.