Former Man City manager Reid, who has a managerial consultant role at Wigan, was forced to step in to separate them as the row over Fabian Delph’s red card continued into the half-time break.
Delph’s sending off sparked a strong reaction from his boss, who not only berated match officials but also turned on Wigan boss Cook.
City went on to lose the FA Cup fifth round tie 1-0, with Will Grigg’s second-half goal at the DW Stadium sealing a famous victory for the hosts.
But the post-match talk has been dominated by Guardiola and Cook’s clash, as well as a mass pitch invasion which saw Sergio Aguero involved in a tussle with a Wigan fan.
But Reid has played down the reports and insists the managers were on good terms after the half-time flashpoint.
Asked about his supposed peace-making role by talkSPORT host Jim White, Reid – who had a famously fiery reputation as a player – said: “I’ve been called many things in my life, but never a peacemaker!
“Pep Guardiola and Paul Cook are two good managers – Pep’s record is fantastic – but what they are is competitive.
“A slight disagreement about the sending off slipped into the tunnel, but it happens. There are cameras in the tunnel now and it’s a massive media game and it gets highlighted.
“I cannot tell you how many times it used to go off in the tunnel when I played, it was virtually every week.
“It shouldn’t happen, but that competitive edge of football which I still love sometimes spills over.
“Something happened last night in the tunnel, so what? We get on with it.
“Do you know what the pleasing thing was? When the final whistle went, the two managers shook hands with each other – that says it all to me.”
Reid also responded to Cardiff City manager Neil Warnock’s claims that Guardiola gets preferential treatment and is unlikely to be punished despite his conduct in the cup defeat.
He added: “Pep is a great manager and wants to win. Does he get special treatment? I don’t think so.
“Coaching these days, because of the media interest, because there are press conferences every other day, people jump on it.
“He is good for English football and good for world football.”