Norwegian marksman Agdestein insists the former Hibs and Falkirk manager has been true to his work in changing very little to the team that was guided into second place in the Premiership by Butcher.
Hughes enjoyed a full week on the training pitch ahead of the trip to Tynecastle after being appointed just three days before last week's goalless draw at St Mirren.
And Agdestein admits Hughes' arrival has been seamless, with the former Brighton player saying: "Everything has basically been the same, he is a great character.
"He has shown he wants the club to do as well as it has done. He does not want to change much with things going so well as they have been. Training has been basically the same.
"Maybe a few training drills and things like that are a bit different but that's about it.
"He knows that there is nothing he really needs to change because of how well we've done. You don't want to change a winning team, as he hasn't done."
Hughes is regarded as one of Scottish football's larger-than-life characters, while Butcher was colourful in his own right.
Agdestein added: "The new gaffer has settled in very well, he's quite a funny guy. He tries to make it fun on the training ground, as well as serious.
"I've not seen a bad side to him yet."
After a tight first half, Northern Ireland international McKay broke the deadlock in the 59th minute with a cool finish from inside the box after edging past Jamie Hamill.
He sealed the win in the 83rd minute by grabbing his 15th of the season with a clinical drive from 18 yards that found the top corner.
"We lifted it in the second half, we started off a bit slow but we did the basics very well, we worked very hard like we used to do," Agdestein said.
Hearts manager Gary Locke, whose side remain 14 points adrift at the Premiership basement, added: "I thought we competed well but the difference between the two teams is obviously Billy McKay.
"I don't think there was anything in the game but with a striker of that quality, he had two chances and he put them away."