The Gunners were left to rue a host of missed chances against Sean Dyche’s men at Turf Moor.
Arsenal have now drawn 13 league games, the most after 25 Premier League matches, and have recorded their sixth successive away draw.
Speaking to Sky Sports after the game, Arteta believes the North Londoners have shown remarkable resilience in defence, but they have to improve at the other end of the pitch.
"The way the boys defended was really good and I think we have improved a lot in the way we concede chances,” the 37-year-old said.
"I learned a lot about the resilience we showed in defence and also that we need to improve the quality of our play, be calmer and improve the end product.”
"In the offensive part of our game, we have to do better for longer periods of the game."
"In periods of the game, yes I liked it, but in other periods I did not. We started to give free-kicks, throw-ins, corners away and in that they are better than us.”
Arsenal now sit tenth on the Premier League table and are 10 points off Chelsea, who occupy the coveted fourth position.
