The club parted ways with Anthony just 10 games into the 2018-19 campaign, causing the veteran to warn Paul that he may suffer a similar fate.
"No, I wasn't surprised at all," Anthony told ESPN's Nick Friedell. "When my situation happened in Houston, he was the first person that I called to come to my room. And we had to clear some things up, and I wanted to know if he had anything to do with it.
"And that was the first thing that I wanted to know, and he told me, 'No.' And from that point on, I told him, looked him in his eyes and said, 'Look, just be careful.' You know what I mean? Just be careful. And damn sure if (the same situation) didn't happen to him."
The point guard said earlier in December that he was caught off guard by the trade after general manager Daryl Morey apparently reassured Paul that he wasn't leaving Houston.
Anthony was also hurt by the circumstances surrounding his departure from the Rockets and made sure he was available to support Paul following the trade.
"He was in Vegas when all of that happened, so we was talking," Anthony said. "And when I talked to him, he was like, 'Man, look, I understand it. It's messed up, but I understand it.'
"And for me, I'm like, 'Yo, it took me months to kind of, like, get past that.' My pride was hit. My ego was hit. I had to really get past that. To a point where it was like, 'Man, Chris, is you good?' I wanted to make sure he was good. So he told me he was good, and that was that."