The Clarets held their own against Arsene Wenger's men for the majority of the game, but once Alexis Sanchez broke the deadlock it was all one-way traffic as the Gunners showed their quality to seal the victory.
Dyche told BBC Sport: "There is a reality to our challenge and that is not the reality, that is the top end of the market. They are a high quality side. They create chances and it could have been more but that is just by the nature of the quality of their players.
"We had been solid before Tom Heaton had to make great saves but after they scored they opened the game up. They get in great passing lanes, they have a great shape, they have pace, power and energy but they also have tactical awareness.
"It not just about one win. We need more than one win, make no mistake. It has to be. That is the challenge. The improvements are marginal it is the learning curve, it is a high state of learning in the Premier League."