The hosts had entered the final Test of the summer series with momentum on their side, having come from 1-0 down to lead the four-Test series 2-1, but were undone by a resurgent Pakistan as they cruised to a 10-wicket victory in London.
"It was really disappointing to finish the series with defeat at The Oval, but we also know how well we did to fight back from 1-0 down against a Pakistan side packed with quality," Bairstow said in his column for the Daily Mail.
"A 2-2 draw is no disgrace and, looking back, there was a lot of physical and mental tiredness after the [third] Test at Edgbaston. We came from behind to win that game, and it took plenty out of us. The Oval Test started just three days later and we didn't do ourselves justice. We didn't live up to our capabilities.
"We know there are areas for us to improve and this was a reminder of how tough it is going to be in India this winter if we're not on top of our game. And that's not necessarily a bad thing. We respond well to adversity. There's a fighting spirit in this team."
England now face Pakistan in five ODIs and one T20 match, before travelling to Bangladesh and India towards the end of the year.