The Cote d'Ivoire international was over the moon with his side's qualification for the knockout stages following Wednesday's win over Inter
Doumbia opened the scoring shortly after the half-time break, but Esteban Cambiasso immediately restored parity at San Siro. However, Vasili Berezutski helped CSKA to the full three points with his goal in the 86th minute.
"I'm really happy because I've been waiting for this moment – we fought tooth and nail until the very end and finally managed to qualify," Doumbia told Uefa.com.
"At half-time I took a peek at my phone to see what was happening in Lille and I saw that the other sides hadn't scored yet; it was still 0-0. So I said to myself: 'Right you've got to give it everything you've got for the next 45 minutes because you never know.'
"And the next thing you know. I was so happy when we scored that second, but I didn't want to get too carried away because we didn't know what was happening in Lille. We had to see our match out and then see what happened in the other game. But when it was all over and we realised we'd gone through it was a magnificent feeling."
The draw for the Champions League round of 16 takes place on December 16.