The BT Sport pundits casually discussed the approach of both sides at half-time thinking they were off-air, however viewers accessing the online stream were able to watch the studio feed.
Cole was discussing pressing the opposition when he brought up Popovic.
"Everyone thinks that Barcelona are great at pressing. Yeah they was [sic], because it was all done properly ... You get them mad English coaches who are just like 'press! press! press!', you do that for 15 minutes and you get them Tony Popovic round and you don't know what's going on," Cole said.
It is unclear why Cole referenced the former Socceroos defender, although fellow pundit and former Manchester City and QPR defender Nedum Onuoha seemed to laugh knowingly.
Cole did play against Popovic at least once, in 2004 when Crystal Palace played Chelsea in the Premier League, while Cole was also an unused substitute in England's 3-1 loss to the Socceroos in 2003 at Upton Park - a match in which Popovic scored.
The leaked footage also shows Ferdinand and Cole being critical of City's right-back Kyle Walker.
"Look at Kyle Walker, sleeping. Look at Kyle Walker," Ferdinand said.
"That's why England - whenever he plays - he'll always be a liability at the top level."
Former Chelsea midfielder Cole agreed: "I'm with you, I'm not saying that though because his mate comes to the gym."
"Everyone talks about this Man City team being perfect, it's not perfect. They will gift you that. They will give you that quick attack because Kyle Walker is playing as a winger."
Ferdinand replied: "You always know that you will get an opportunity against them, but you have to be clinical like they were today. If you've got the bollocks."
Cole then concluded: "And that's why the good teams can hurt them because they've got players like [Eden] Hazard."
