Hartley, who was in charge of the Bairns in 2017/18, did similar after the reverse fixture at the Falkirk Stadium back in November.
Miller was speaking to the press after the 2-0 defeat for the Bairns which saw their lead at the top slip to just goal difference over Rangers.
Five players were booked during a match that got fiery without ever really boiling over and Miller, who came on as a substitute for the final 15 minutes, felt the Cove players went down too easy at times.
He said: "There was a lot of throwing themselves to the deck that I saw.
"Was there a nastiness? I don't think so, with two teams fighting at the top of the league it's always going to be like that.
"The thing that did disappoint me was the manager didn't stay to shake hands again, I think that's classless.
"It's one of those things, no matter what happens win, lose or draw you always stay to shake hands."
It was a disappointing afternoon all round for the Bairns as the two goals they conceded both came from set plays, something that is becoming an all too familiar occurrence.
"We never got started today,” said Miler.
"We had a game plan in place and never really took it to Cove, I don't think we started the game right and it took us a while to get into it.
"Set pieces are your bread and butter, you need to be aggressive in both boxes and I don't think we did that today.
"It's something we need to look at, to play goals can be eradicated.
"You have to do the basics right and the rest take care of itself, we didn't do that today."
Cove manager Paul Hartley said after the match he didn’t feel the win over his old club was sweeter than any other victory.
He said: "I never see it like that, there's no revenge in it for me.
"It's another game and another three points."