The Spanish side looked poised to take a 1-0 advantage back to the Bernabeu thanks to Cristiano Ronaldo's first-half strike but Pontus Wernbloom leveled in stoppage time to ensure the tie remained finely balanced.
Mourinho said: "Their goal was frustrating, but we earned a good result I'd be happy to have in every knockout tie in which we play the return leg at home.
"Their strike made them very happy and we were frustrated by it because we played for more and had chances to score more.
"Our opponents made things very difficult for us, but they did little to score or draw the match. They played a serious and tough game. They worked very hard."
Another blow for Madrid was the early departure of Karim Benzema with an injury, but on the artificial surface and in freezing temperatures Mourinho was pleased it was not worse.
"I actually thought that if we were to sustain injuries we could have sustained up to three, but in the end only Benzema was injured," he said.
Midfielder Xabi Alonso claimed CSKA's equalizer should not have stood.
"We all saw Ronaldo was fouled before their equalizer, but we shouldn't dwell on it," he told www.realmadrid.com. "Our opponents also did a good job and [we] practically had no trouble until they scored. We are confident to win the tie in the return leg.
"We clearly expected a better result seeing how the game unfolded. The draw isn't a bad result, but it could have been better."