The Gunners won 3-2 on Sunday, with Odegaard scoring the winning goal from the penalty spot, which was earned by Dowman's contribution.
Odegaard acknowledged the challenges of playing in the heat and against a strong opponent, but expressed satisfaction with the team's performance.
"It was a tough game, physically and against a strong team," he said.
"We played some good football in the first half and controlled the game, but the second half was a bit more open."
Odegaard praised his teammates, including Dowman, who made a positive impact when he came on.
"There are a lot of positive things to take from this game," Odegaard said.