Goals from Juan Iturbe and Maicon, and a Gervinho brace saw Roma race into a 4-0 half-time lead in the Group E fixture at the Stadio Olimpico on Wednesday.
Sergei Ignashevich's own goal made it five just after the interval, before Ahmed Musa scored a late consolation.
Roma were imperious as they made a dream start to their first Champions League campaign since 2010-11, but injuries to Argentinean midfielder Iturbe and Italian defender Davide Astori gave the coach cause for concern.
"It was a great performance, we won and got the three points," he is quoted as telling Sport Mediaset. "It is just a pity about the injuries, but Roma's performance for 75 minutes was beautiful and efficient.
"Astori has a sprained knee and Iturbe a muscular problem. We will have tests over the next few days and hope they are nothing too serious."
And the Frenchman says the result will send Roma into their next Champions League match - a trip to Manchester City in a fortnight's time - with renewed confidence.
"We knew that even if the result is important, CSKA are not the weakest team," he continued. "This is why I want to underline our great performance.
"It seemed easy by the result, but wasn't remotely easy beforehand.
"When you start on home turf, it is fundamental to get the three points.
"We started on the right foot – maybe two right feet – and now we go to Manchester with more confidence."
But Garcia stressed his main focus was now on a return to domestic competition.
"We’ll see, as right now we have to concentrate 100 per cent on the next game with Cagliari," he added. Fortunately we have a large enough squad to face every competition at our best and we want to win every game."
