The Russians had taken the lead, but second half goals from Hernan Crespo and Walter Samuel - the latter aided by a Veniamin Mandrykin howler - turned it around.
This was an important win in a tough arena and was definitely deserved," said Mancini. "After conceding their goal, which was acceptable because we were facing a strong opponent, we were the only ones who took the initiative and could have scored more goals.
"CSKA started well today and put us under pressure, but the important thing was to have the upper hand at the final whistle. We cannot expect to dominate matches for 90 minutes.
"We are not qualified yet, but tonight we picked up three very important points," said Mancini. "Now our group can be decided over the next home games that await us."
Crespo equalised, but was almost immediately then replaced by Julio Cruz at the Lokomotiv Stadium.
"It is of course great to have strikers who have the quality to change a game. Crespo is always decisive, even when he's not in top shape, as he only needs one chance to score. Clearly nobody likes to be substituted, but at that moment I had to make a change."