The Russian side snatched a precious away goal through Vagner Love – his ninth strike in seven European games this season.
But John Carew’s second-half effort has given the midlands club a lifeline for the return meeting next Thursday.
Villa have shown they are more effective away from Villa Park this season with 10 victories in the Premier League on their travels.
O’Neill said: “We have still got a chance although obviously it will be really hard in Moscow.
“They’ve scored the away goal and you’d think it was all doom and gloom but it’s far from it.
“They have an away goal so we have to score to have a chance but it is not impossible.
“They showed they are a dangerous counter-attacking side but so are we as our record has shown this season.
“They are a very good side who won their group in a canter and have already qualified for the Champions League.’’
He added: “But I thought we played really well and deserved to win this game. I thought we deserved to win. We created a great number of chances and played with great spirit.
“I thought we were terrific, although we defended poorly for Love’s goal.
“The players are learning all the time, gaining experience from playing in Europe and I was really pleased with them.
“People say we are hard working and determined but we also have some real quality in this team and have showed this all season. If we had been beaten I would have been disappointed.”
Carew agreed with O’Neill’s sentiments stating: “European games are very difficult, and we were against a great team, so we can’t be disappointed.
“It was a good game in the end but the away game will be more difficult, and cold, so we will have to prepare well and believe we can do it, although it would have been good to get the win today.”
O’Neill again highlighted the problems caused by left winger Ashley Young, who tested the CSKA defence with a series of menacing crosses.
O’Neill said: “Ashley delivers such a quality ball. If I was playing now, I would score 29 goals a season with someone like him to feed off!
“He is an exceptional deliverer of the ball.”
CSKA coach Zico believes his side will benefit from an extra week’s training ahead of the second leg after playing their first competitive match since December 4.
He said: “It was a highly competitive game. Our team resisted greatly. It was a good result for us.
“Nothing is resolved yet and we will do our best. The next game we will be in better condition and more ready to play another game after the break.
“We were not surprised by the way Villa played. It was very seldom they had the ball on the ground making passes.
“They get Ashley Young to put the ball into the box a lot. We expected this sort of game and we were ready for it.”
ASTON VILLA: Guzan, Luke Young, Davies, Knight, Shorey, Gardner, Petrov, Barry, Ashley Young, Carew, Agbonlahor.
CSKA MOSCOW: Akinfeev, Berezutsky, Ignashevich, Berezutsky, Shchennikov, Krasic, Rahimic, Aldonin (Mamaev 90), Zhirkov (Erkin 92), Dzagoev (Daniel Carvalho 80), Vagner Love.
Referee: Peter Rasmussen