The Pumas secured their biggest win over the Wallabies and their most emphatic in the Rugby Championship, winning 48-17 at Estadio Bicentenario.
Australian Cheika coached his country for five years before his reign came to an end in 2019 and the 55 year-old had mixed emotions during a record victory for Argentina in San Juan.
The Argentina coach told reporters: "I love these guys, they're my crew now. I was up on the last try, cheering. But then I started crying because I know I probably shouldn't be doing this. It was a bit confusing for me, personally.
"But they're my boys now. That's my team. I will do everything I can to help them get success and enjoy rugby.
"They are paying me a lot of respect here and people are believing in the things that we are doing. I have to do everything I can to help them."
Cheika is relishing a short break in his homeland before Argentina takes on New Zealand.
"It's good to be going to Australia and have a few days off, seeing my mum and my brothers and sisters and take the boys for a Leb (Lebanese) feed at my mum's place," Cheika said. "But I am looking forward to going to New Zealand because it is a great place to go and play rugby."