Mackay was sacked by Cardiff on Friday, less than 24 hours after the 3-0 Boxing Day defeat to Southampton.
The Scot's exit has been on the cards since he and owner Vincent Tan fell out over the dismissal of head of recruitment Iain Moody in October.
Since then Mackay had seen his hopes of strengthening his squad in January rebuffed by Tan, who sent his manager an ultimatum to resign or be sacked.
That threat was briefly lifted by a statement from chairman Mehmet Dalman which said Mackay would in charge for the "foreseeable future". As it turned out, he was sacked just five days later.
Rodgers, who worked with Mackay at Watford, had previously accused Cardiff owner Tan of knowing nothing about football, but admitted his former colleague's exit came as no surprise.
Rodgers said: "Of course it is a sad day for him but it is something he probably felt was on the cards for him anyway.
"So I think it is best for him that there is closure on that.
"Certainly he is a guy that has given that club so much. He will go down in history as the manager that has taken them to the Barclays Premier League and - at this moment in time - the greatest manager in their history.
"He will move on. He is going to be an outstanding manager for many years at the top level.
"He will recover and come back fighting and show that he is the great manager he is."
Norwich manager Chris Hughton echoed Rodgers' comments when asked what he made of the dismissals of Mackay and Millwall boss Steve Lomas.
"It is very disappointing, on both managers," said the Canaries boss.
"But I think with Malky it is not a massive surprise because of everything which has been talked about over the past few weeks and the pressure that Malky was managing under.
"I am very disappointed for him and it is a saga which has gone on for the last couple of weeks and is one I don't think it one which could have been doing anyone any good."
Other prominent figures within the game took to Twitter to voice their criticism of the decision to part with Mackay.
Former England striker and Match of the Day host Gary Lineker tweeted: "It will be fascinating to see who Tan now appoints. Anything could happen. Fear for Cardiff!"
Ex-Liverpool and England forward Michael Owen posted: "I guess it was inevitable that Malky Mackay has finally been sacked. A real shame after doing such a great job at Cardiff City."
Iwan Roberts, a team-mate of Mackay's during the Scot's time at Norwich, tweeted: "Gutted for big Malky he can hold his head up high and leave with dignity.Horrendous working circumstances for him to work in!"
There were also comments from those outside the sporting field, with Leighton Andrews, Welsh Assembly Member for the Rhondda, tweeted: "The club has sacked the best manager we have had in a generation on the eve of a crucial game. #ccfc #bluebirds #ridiculous".