The Gunners saw their title hopes suffer a serious blow at the weekend as they were brushed aside by their London rivals at Stamford Bridge.
However, Podolski is confident that he and his teammates still have the chance to be crowned champions at the end of the season.
"We are all very disappointed. Chelsea showed the right attitude and from the first second, how much they wanted it. They were present from the beginning and left us no chance," he told the German national team's official website.
"For first place it is brutally tight, and yet we still in touch. We need to continue to play better than we did against Chelsea.
"Above all, we must continue to believe in our strengths. Chelsea was a setback – but we must not now let them destroy us with talk."
Arsenal have the opportunity to get back to winning ways tonight when they host Swansea City in the Premier League.