The former Real Madrid man produced a sublime 30th-minute effort which sailed into the top corner of the net at Turf Moor, and Arsenal held on to grind out their second 1-0 win of the Premier League season.
Speaking to BBC Sport, Odegaard said: "When we got the free-kick I immediately went to the ball. It was a big moment and a nice moment to see it go in. You need to hit it pretty perfectly, with the right speed and the right height.
"The game was kind of a war in the end. We know their strength. We played their game a little more than our own game. In the second half they played their game and they're good at it. We need to be a little bit smarter when we win the ball.
"I believe in this team. Even though we lost some games in the beginning, I'm not too surprised we've got some points now."
Arsenal have temporarily moved up to 12th in the Premier League table and now prepare to take on AFC Wimbledon in the EFL Cup on Wednesday. body check tags ::