Spurs were comfortable 3-0 winners on Saturday via goals from Richarlson, twice, and Brennan Johnson.
"I thought there were plenty of positives to take, despite the defeat," said Parker.
"We started slowly, we were really under pressure, but then after they got their noses in front, I thought we really grew into the game.
"There was a real impetus about us, we played on the front foot and looked a real threat, our reaction and endeavour was superb.
"The clinical and ruthless nature of the Premier League was then there for everyone to see just before the hour. We had two massive, massive chances, where we just weren't ruthless enough, and then they go up the other end, create a half-chance, and double their lead with a world class finish.
"They're the fine margins - that's this division really."
Parker added: "I can't fault the lads at all. They played on the front foot, showed great endeavour.
"It'll be a massive challenge for us this year. Games like today won't define us - we'll learn, we'll bounce back, and we'll look forward to being back at Turf Moor next weekend."