The Serie A side appeared set to move three points clear of CSKA and five clear of Manchester City in Group E - ahead of the English champions' home game with Bayern Munich - thanks to Francesco Totti's first-half free-kick at Arena Khimki.
However, hosts CSKA grabbed a dramatic leveller to keep their own qualification hopes alive, Vasili Berezutski finding the net in the third minute of stoppage time when an apparent cross from the left drifted beyond two attackers and Roma goalkeeper Morgan De Sanctis.
Garcia was understandably frustrated by Berezutski's goal, but underlined the fact Roma are still in control of their own destiny given their superior head-to-head record against CSKA.
"When you fail to score a second, you always risk conceding like that. We needed to put the game to bed. It's a shame," Roma's coach is quoted as saying by the club's official Twitter account.
"No matter what happens in Manchester [in the game between City and Bayern], we need to win our last game [at home to City] to qualify from the group, which is our goal.
"No-one gave us a prayer after the draw. But we're in with a shout in the last game - it's a fantastic opportunity for us."
Roma saw two golden chances go begging prior to CSKA's equaliser, as Radja Nainggolan fired wide with the goal gaping and Igor Akinfeev made a fine save with his left boot to deny Adem Ljajic.
Garcia added: "Ljajic and Nainggolan both had chances to score. I'm disappointed, though an away draw is not a bad result."
Alessandro Florenzi, who started at right-back against CSKA, also expressed mixed emotions.
"A draw is almost a fair result, because after the break we weren't the same team as in the first half," said Florenzi.
"It hurts to concede with 15 seconds to go.
"If we play like we did in the first half, that will be enough to beat Manchester City."
