The Reds were pegged back in the second period as Victor Wanyama's fine long-distance strike cancelled out Mohamed Salah's third-minute opener.
But they looked to have won it at the death when, after Loris Karius had saved a Harry Kane penalty, Salah scored an incredible individual goal, weaving through the Spurs defence before finishing smartly.
However, Mauricio Pochettino's team were awarded another spot-kick in the third minute of injury time, and Kane made no mistake this time to ensure the score finished 2-2.
Reflecting on the game, Milner told the BBC: "We played well first half, second half they got on top a bit and it was hard for us to keep the ball.