The Premier League champions suffered their third defeat in their last four matches in all competitions after George Boyd???s strike gave the Clarets victory at Turf Moor.
The result leaves City five points behind leaders Chelsea but having played two games more.
Asked whether something is wrong, Pellegrini told Sky Sports: ???Of course. We are doing something wrong, we are not winning the games we normally do, especially against this kind of team who have been very difficult for us. We are not scoring goals.???
The 1-0 defeat marks the first time City have failed to score away from home in the Premier League in over a year.
But Pellegrini refused to be drawn on their late claim for a penalty when Ben Mee appeared to foul Pablo Zabaleta in the area.
???Maybe (it is a penalty) but it is the referee who decides,” he said. “I don???t have a strong view and I don???t want to talk about the decision because I don???t think that is the most important thing of the game.
???We were a little bit flat but we tried to create more chances and more space. We had three or four chances to score, they had just one on target and scored a beautiful goal.???
Boyd???s fantastic strike from the edge of the area leaves City???s title hopes hanging by a thread, but Pellegrini is not writing off his side yet.
???When you have a mathematical chance it is possible, but in reality it is more difficult,??? he said.
???It???s important to continue trusting in what we are doing, the chance for the title is far but we must try to continue fighting for our position and we have an important game against Barcelona (in the Champions League on Wednesday).”