Murray headed the equaliser in yesterday's 1-1 draw with Southampton after Steven Davis gave the visitors an early lead when James Ward-Prowse's free kick came back off a post.
The Seagulls sit 12th in the top flight after ten league games and reflecting on Brighton's start to life in the Premier League, Murray said: "I think we're doing well, as a group we can be happy and I feel we're always improving and learning about the league and we're enjoying the task."
The draw with Southampton was the first time this season Albion have trailed in a game and fought back to get a point and Murray said: "It's good and we've got to take positives out of it. The main lesson we've got to learn is the first goal is so important. To give that away at home was a little bit disappointing.
"It was a good free kick, he got it up and over the wall. Unfortunately for us, Southampton were quicker to react and got the goal."
Murray's goal was his 50th at home for the Seagulls. He netted on his home debut for the club at the Withdean Stadium nine years ago and on reaching the home landmark said: "These things are nice but it's all about the team and it's all about picking up points in the Premier League."