The Blues' impressive home run against their London rivals, seeing them comfortably win this fixture five seasons in a row, came to an end on Sunday afternoon as they failed to find a way through.
Azpilicueta had mixed feelings on the back of the stalemate at Stamford Bridge, having seen his side slip three points behind early pacesetters Manchester United and Manchester City at the Premier League summit.
"We can do better, that's true. We will keep working hard to improve and to become a better team," he told reporters. "In the last few years at Stamford Bridge, we have won the games [against Arsenal] and found space to create chances for our strikers.
"Yesterday was a bit more complicated. They played a good defensive game where everyone was working hard and they made it difficult for us. It's a long season and we are still only in September. Every point counts. Obviously a win is better than a draw and a draw is better than a loss.
"We weren't able to win against a good team, but we didn't lose either and that is important. Now we have to move on. We have a cup game in a few days, the season keeps rolling and we cannot stop."
Chelsea have a chance to respond to their first home draw under boss Antonio Conte when facing Nottingham Forest in the EFL Cup on Wednesday night.