Max's superb solo effort gave Scotland hope of staging a sensational late comeback as they battled to end their 28-year wait for a win in London.
The Glasgow back's try was his third for his country, with his previous two also coming in defeats, against Wales in 2009 and 2010.
Describing his touchdown as an "opportunist" effort, he said: "It would have been nice for it to be the winning try.
"There was definitely a feeling we could go on and win it," said the wing, who had no doubt where Scotland lost today's game.
"Our defence was just immense but the frustration is that set piece.
"To lose it so easily and on numerous occasions is just hugely frustrating, especially from a backs point of view."
Scotland were well in the game until John Barclay was sin-binned midway through the second half, with England scoring their try seconds before the flanker re-entered the fray.
The Glasgow breakaway forward was penalised for knocking the ball away as England attempted to recycle and Max said: "From what I hear, the feeling is that it was slightly unjustified.
"I hear that John was clearly over the ball and competing for the ball."