Speaking after Bafana Bafana's arrival at OR Tambo International Airport on Thursday morning, McKenzie hailed Broos as the man who transformed the national team from a laughing stock into one capable of competing on football's biggest stage.
South Africa made history by reaching the knockout stages of the FIFA World Cup for the first time before their impressive run ended with a narrow 1-0 defeat to Canada in the Round of 32.
McKenzie believes the achievement is a testament to Broos' remarkable work since taking charge of the national team.
"The first thing we must be honest about... Before Hugo Broos came here, Bafana Bafana was a joke. People laughed at us, nobody took us seriously," McKenzie told IOL.
"When Hugo Broos came, he lifted us up. What Hugo Broos has done for our football... we need to build a statue for him because Hugo Broos has really done so much for our football."
While expressing hope that Broos remains in charge, McKenzie admitted the coach's future depends on personal discussions with his family.
However, he made it clear who he believes should take over if Broos decides to walk away.
"If Hugo Broos does not stay, there is only one man for the job. Pitso Mosimane. I am unapologetic about it. That job must be given to Pitso."
South Africa exceeded expectations throughout the tournament by finishing second in their group to qualify directly for the knockout rounds, rather than relying on a best third-placed finish.
It was another landmark achievement for a nation that had not qualified for the World Cup on merit since the 2002 tournament, further highlighting the progress made under Broos' leadership.
Bafana Bafana captain Ronwen Williams admits the pain of their painful FIFA World Cup exit will linger after South Africa conceded a dramatic stoppage-time goal against Canada in the Round of 32.
Portugal head coach Roberto Martinez said his side were ready to begin what he described as a "second World Cup" as they prepared to face Croatia in the Round of 32 in Toronto on Thursday.
Oswin Appollis' absence from Bafana Bafana's return to South Africa has intensified speculation that the Orlando Pirates winger could be on the verge of securing an overseas move.
Norway manager Stale Solbakken has insisted his team had nothing but respect for Brazil coach Carlo Ancelotti ahead of their FIFA World Cup last-16 meeting, explaining that a viral dressing-room video was never intended to provoke the Italian.
