The Saints lead Middlesbrough by a point at the top of the Championship after substitute Morgan Schneiderlin's late equaliser at Turf Moor.
"With 80 minutes gone and 1-0 down away from home Morgan Schneiderlin scores a goal, and it's a point gained, but when you look at it we had a great passage of play," Adkins told the club's official website.
"As the second half as gone on it shows how fit we are because we've totally dominated that. It was first half to Burnley - second half to us.
"Is a point a fair reflection of the game? I don't know, but we could have won it."
Southampton's next game is a trip to Cardiff City on Wednesday night.