Warnock appeared to remonstrate with Sarri at one point but the Cardiff boss said the exchange was amenable.
"He's lovely. He was moaning about a throw-in or something," Warnock said.
"I said 'Do you not know he's two yards offside! You should be patting him on the back, not complaining about a throw-in.'
"He [Sarri] didn't realise he [Azpilicueta] was offside, he said.
"The game is passion. I'm 70 bloody years old. If you're not passionate at my age when you see such an injustice when you've seen the lads battle and fight like they have… against a team we should have beaten," he said.
"Do you expect meek and mild and 'congratulations Sarri', patting him on the back? And shake the referee and linesmen's hands? Come on, it's the Premier League, it's the best league in the world. And we are disappointed."