Mendy made his first Premier League start since September 2017 at the Emirates Stadium having missed the vast majority of last season through injury, helping City to a clean sheet as their title defence got off to a victorious start.
The French full-back is a renowned presence on social media, but Guardiola urged him to focus more on matters on the pitch and warned him that he has plenty of things to work on.
"Mendy is Mendy. Sometimes you want to kill him. Sometimes you say, 'Wow, what a player'," he told reporters.
"Mendy has a lot of things to improve. Hopefully we can convince him to be calm and forget a bit the social media and focus on what he has to do."
Mendy's injury last season means that he has been limited to just 10 appearances for the club since his £52m move from Monaco in 2017.