Key was also a guest on the the TMS programme and he said England will make changes in the way they approach selection.
There had been a perception that the England Test team felt like a ‘closed shop’, particularly to players in county cricket who did not fit the aggressive Bazball style.
Key said the introduction of a “county insight group” to offer insight into selection will attempt to formally rebuild relations with stakeholders, including directors of cricket, in the domestic game.
The 46-year-old former Kent captain also said England’s selection policy will become more cut-throat compared to the past when certain players have almost appeared undroppable.
“We’ve overvalued loyalty and overvalued having a settled team,” Key said.
“We thought what we wanted to do is make sure we have a team that is settled out there [in Australia], that we go out there and we’re not giving debuts to opening batters [during the Ashes] and stuff like that.
“But what that does is it creates an environment where there’s not enough consequence. We need to be more ruthless with our selection.”
McCullum is due to return to work towards the end of May as England gear up for a Test series against his native New Zealand which starts at Lord’s on 4 June.
However, Vaughan felt it would have been worthwhile McCullum spending time on the circuit during the early rounds of the County Championship – for good PR if nothing else.
“I’m a bit disappointed that he’s not coming a bit earlier,” Vaughan said.
“I think at this stage, when you’re trying to win back the fans, trying to win back a little bit of the game, if I was Brendon McCullum, I’d come a few weeks earlier, get seen around the counties.
“I’d go and talk to a few coaches, go and speak to a few umpires, get seen out and about just for the optics. Because at this stage he needs the fans, and he needs the game to kind of get behind his philosophy a little bit more.”
You can watch the full TMS debate over the post-Ashes review on BBC iPlayer or download it as a podcast.