City looked in command of their latest Group E assignment in the Russian capital - one they were anxious to win to ignite a faltering campaign - but were held 2-2 after conceding a controversial late penalty.
Pellegrini initially appeared to suggest his team got over-confident, by referring to "an excess of trust", and that the freezing temperatures may have affected his team in the second half at the near-empty Khimki Arena.
But when pressed further, he insisted he was not trying to make excuses for his side's third frustrating result in the competition this season.
The Chilean said: "The cold was exactly the same in the first half as the second half.
"The first half we played really well, scored two goals and had other chances to score
In the second half, maybe for different reasons, we couldn't do it.
"I don't like to give different excuses about what happened
I think we had it all to win and we didn't."
Pellegrini, when first asked to give his reaction at his post-match press conference, had said his team did not capitalise on the excellent start which brought goals for Sergio Aguero and James Milner.
He said: "Of course I am very disappointed, not only because we were winning 2-0 at the end of the first half, because we had three or four chances to score.
"I think the first half was a minimum three or four goals difference, but football finishes in minute 95 and we allowed CSKA to draw.
"I think we didn't play well in the second half
Maybe an excess of trust or it was so cold it was difficult to continue motivation for the whole game.
"I think we did well in the first half and maybe it was too cold in the second."
CSKA pulled one back through Seydou Doumbia before the same player won a penalty after going down under a challenge from Aleksandar Kolarov.
City were unhappy with the decision but Pellegrini, who received a touchline ban after complaining about a referee last season, did not offer an opinion on the incident.
"I don't want to talk about that," he said.
Goalkeeper Joe Hart did express his frustration about the penalty - which was converted by Berbas Natcho - but felt City should already have made the game safe.
Hart said: "I don't think it was a foul but Aleks gave the referee a decision to make
We thought it was the wrong one, but a lot more could have been done before that to get the result."
Hart added that City only had themselves to blame for allowing CSKA back into the game.
He said: "It was a difficult game - we played well in the first half but in the second half were too open, but it was a fair result.
"It was really cold in the first half, when having the wind in your face made a big change, but the second half was fine.
"They are not excuses, it was the same for both teams - unfortunately we didn't play well enough."
City have now collected just two points from their opening three games in the competition and will face a battle to qualify for the latter stages.
Both Hart and Pellegrini remain confident that can be achieved.
Hart said: "It's going to be difficult but we are capable of qualifying from this group.
"We have a home game against Moscow now and have to focus on that first and let the other two do what they need to do."
Pellegrini said: "I trust in this group
I am sure we are going to qualify for the next stage
We will see in the next game what happens
In December we can talk about different things.
"Now we have nine points more to play for and I hope we will see the team that you saw in the first 45 minutes and the team you see every weekend in the Premier League.
"There is a lot more to fight for and we will fight to the end."
CSKA coach Leonid Slutsky was pleased with his side's fightback.
He said: "In the first half we did not play so well and the first moment for Manchester City was a goal.
"But we made a few changes, we changed a player and the system.
"Things started to go well and I am happy with the overall result."
Source: PA