Clarets boss Sean Dyche bemoaned two soft goals which derailed his brave side at Arsenal.
Burnley were 19 minutes away from a precious point at the Emirates before 5ft 7ins Chilean street fighter Alexis Sanchez headed in a Callum Chambers cross, and Chambers himself prodded in a second from a corner a minute later.
Sanchez, signed from Barcelona in the summer for £35m, added a sheen to the score line, and Dyche said: “We could have not given away two soft goals. Other than that I think the team operated in a very good manner.
“Its a very tough place to come, and tactically we delivered, certainly for 70 minutes, and the reality was there for all to see.
“They get their noses in front and it’s very hard then. They’re clinical, they have pace, cleverness and quality everywhere.
“We know that’s not our real market, we’ve played six out of the top 10 so far, and we’re not ready for them, we’re ready for a different market.
“But its important we learn from it and improve.”
The defeat means Burnley have started their Premier League campaign without a win in 10 games, but Dyche admitted: “It’s a high state of learning myself and the players are in, and we have to learn quickly, there’s no naivety. I understand the market we’re in, we’ve got to get results.
“But there has to be a reality in our journey, and that’s beyond that at the moment.”
Goals from crosses and set plays have been a real thorn in Burnley’s side, and Dyche accepted: “You have to look at the quality of the cross and the quality of the run, but the set play goal is a very poor one.
“The first goal - sometimes there is a balance, and I think he (Sanchez) was a couple of quid wasn’t he?
“Usually, they are that much for a reason, and he was excellent all day.”