The club's former owner criticised the Scot's spending during the summer transfer window and urges Vincent Tan to take "complete control"
Mackay was dismissed on Friday following Cardiff’s 3-0 defeat at home to Southampton on Boxing Day, which has left the club one point above the relegation zone after 18 games played.
Tan and Mackay’s relationship had deteriorated over the Christmas period to the point where the Malaysian businessman asked the 41-year-old to either resign or face being sacked.
“The sacking of Malky was the right thing to do, the only problem is it should've been done a long time ago,” Hammam told BBC Wales.
"If they're not... perfectly synchronised and are not working hand in glove, it just simply is not going to work.
"And because Vincent owns the club then Malky has to go. It doesn't matter what is right or wrong, or what Malky did - this is beside the point."
Hammam, who owned the club between 2000 and 2006, claims Mackay received the plaudits for the club’s Championship-winning campaign last term, despite heavy investment from Tan.
"Are we up because of Vincent, or because of Malky?" Hammam continued.
"Well, the answer is because of both. But, by and large in a very, very big percentage it's because of Vincent, but the accolades and so on went to Malky.
"The key here is one word - control.
"It is now high time that Vincent Tan takes full and complete control of all aspects of the club as and when he can."
Former Manchester United striker and current Molde manager Ole Gunnar Solskjaer has been linked with the vacant role and Hammam believes the 40-year-old possesses the experience required to keep Cardiff in the Premier League.
Hammam also criticised Mackay's spending in the summer transfer window after the Scot broke the club's transfer record three times to sign Andreas Cornelius, Steven Caulker and Gary Medel.
"I've known him from when he was a young kid playing for Molde and I tried to buy him when I was the owner of Wimbledon," Hammam said.
"He had a good grounding when he played for Manchester United but significantly now he's the manager for Molde, he would have had very good basic grounding for what is needed now.
"We need a manager whose feet are on the ground and not just telling Vincent Tan, 'give me your money, give me your money' as if Vincent Tan is a cash cow."