The Blues, who fell to a defeat against Burnley on the opening day of the season, have looked much better over recent weeks, claiming three successive wins against Tottenham, Everton and Leicester.
However, that run was ended on Sunday as Arsenal made life tough for them at Stamford Bridge to claim a share of the points.
Cahill felt Chelsea performed well but admitted to feeling frustrated as they failed to create enough clear cut opportunities.
"It is frustrating, a good, competitive London derby. There wasn't much in the game, played in the right manner," Cahill told the BBC.
"We had a lot of possession in the first half and tried to create but it felt frustrating. They defended well, we couldn't open them up."
Chelsea saw David Luiz sent off on 87 minutes and ended a game with 10-men for the third time this season, however, Cahill insists he didn't have a clear view of the incident.
He added: "I didn't see the red card properly but David Luiz thought he was fouled beforehand. We have responded well to losing on the opening day and got some strong results. We take the point and we move on."