Nacer Chadli had fired Spurs ahead in the 56th minute, but the Gunners rallied to secure an equaliser from Alex Oxlade-Chamberlain and earn a share of the spoils at the Emirates Stadium.
Pochettino told Sky Sports News: "I think it is a good result for us. Maybe Arsenal controlled the game and had the ball more than us but we played well and defended well. I am happy with the performance in a tough game. I think the draw is fair.
"We scored a great goal. This is our philosophy, which is difficult to keep for 90 minutes at the moment, but we are on our way."
Tottenham are eighth in the Premier League following their draw.