The contact caused Miller to lose two positions at the time, with both Mir and Enea Bastianini passing the Queenslander.
Miller eventually finished the race in seventh place, as Mir had to drop one place, as he was penalised for the manoeuvre.
The situation got tense with Miller exchanging words on the cool-down lap with Mir.
“Like last time in Misano I finished in one position and then a penalty lifted me a position higher – it’s a story you’ve heard before.” The Australian posted on his blog following the race.
“I crossed the line eighth at the end, but you all saw what happened with Mir on the last lap.
“It was like last time in Misano all over again. I got hit, lost spots to two guys… at Misano he got pushed back a place for track limits, and here it was one place for irresponsible riding.
“Race direction did what they did with him, so there’s not much more to say about it really.
“I was struggling with my front tyre, I tried to protect the line… but you can’t protect when someone runs into the side of you, can you?
“I swear, every time I race with the guy, he seems to run into me. It’s not just the last two races either.
“I think there’s better ways you can go about the situation. I was fading at the end of the race, don’t get me wrong, but that didn’t need to happen.
“Fortunately, I was able to stay on the bike and I felt I controlled myself rather well afterwards.”
Mir and Miller have had history in the past, with the two aggressively racing together on track in Qatar.
Despite the seventh-place finish, Miller has moved up a spot in the championship standings to fourth overall.
Miller will return to the track when MotoGP™ returns to Misano on 22-24 October.