Burnley forward George Boyd scored the decisive goal with a superb half-volley to give the Clarets a deserved victory against the reigning champions on Saturday.
The defeat means City are now five points behind league leaders Chelsea having played two games more than Jose Mourinho’s side.
Should Chelsea win their two matches in hand they would be 11 points clear of City, but Pellegrini refused to concede that they can no longer win the title.
“When you have a mathematical chance, you have a chance to win the title,” he said.
“The reality is that it’s more difficult to do so now. Every point we drop will be more difficult.
“When you have mathematical chances you must continue fighting and see at the end of the season where you will finish.
“We are not worried about just our team. We know every time we drop it is more difficult. We have 27 points more we must fight for.”
The visitors produced a disappointing display as they failed to match the intensity and work-rate of Burnley’s players, particularly in the first half.
City now turn their attention to the second leg of their last 16-tie against Barcelona at the Nou Camp, which they trail 2-1.
And perhaps with that match in mind Pellegrini refused to be critical of the performance of his own players against Burnley, despite being outfought by the Clarets.
“I am sure they tried to give everything,” added the Chilean. “Of course we’re doing something wrong as we are not winning the games we normally do.
“I don’t want to focus on two or three players. We are a team, a squad of 22 players, and I’m sure they’re giving the most they can. It’s important to continue trusting what they are doing.
“I don’t think we played very bad. We had three or four chances. Burnley had just one and had one goal but I don’t think we created enough chances.
“Football is not only money. It is an important thing but any team can win against another in the Premier League. We must create more chances against a team like Burnley.”
Burnley manager Sean Dyche believes the result emphasised just how hungry his players are to remain part of the top flight.
The victory means the Clarets are within a point of safety although Dyche admits his players will not let a result like this go to their heads.
“Our will and desire to be in the Premier League is all on show. But we won’t get too carried away,” Dyche said.
“A lot has been made of this tough run of games. It is a rough run, we know that but it is the challenge we wanted. It is not about the money. We wanted the challenge. When it is the big games, you don’t say ‘oh woe is us.’
“We know there’s a long way to go – the players are grounded. We haven’t been broken from defeat – we’ve been dented a few times – but this win reinforces confidence and belief.
“There is growth in the players and I have said it for many weeks. It doesn’t guarantee our future.”
Dyche also praised the quality of Boyd’s winning goal which he struck on the half-volley after Kieran Trippier’s free-kick had been headed clear by Vincent Kompany.
Dyche added: “George’s was just a magnificent strike, he has got that. It was a clean strike and a fantastic bit of technical work. There were some real strong individual performances, and he was terrific.”