The world champions are in hot water following their celebrations after their final victory over France in Qatar.
Martinez was criticised for appearing to make a vulgar gesture with his Golden Glove award following Argentina’s penalty shoot-out win last month.
He was also filmed in the dressing room mocking France’s Kylian Mbappe, although FIFA has not named any individuals, with Argentina cited for potential misconduct of players and officials and offensive behaviour and violations of the principles of fair play.
Emery admitted he was not aware of the nature of any disciplinary action but reiterated his pride in Martinez.
He said: “It’s two different moments. One moment is for the national team in the World Cup, the other one is here.
“We have values and we try to be respectful, first with us, second with the opposing side and of course with the supporters.
“Before, when we worked in London with Arsenal together, and here he’s a very good guy, respectful. He is very competitive, he came to London when he was 18 years old.
“He has been playing here for 12 years, trying to get to his target which was massive. We have to be so, so proud of him here.
“Me? I am so, so proud of him.”
Martinez helped Villa to a 2-1 Premier League win over Leeds on Friday after goals from Leon Bailey and Emi Buendia.
Villa rode their luck as Leeds created several chances with Alex Moreno clearing off the line from Rodrigo and Martinez denying Jack Harrison and Wilfried Gnonto.
It left Leeds winless in their last seven games in all competitions but boss Jesse Marsch denied they are in relegation trouble.
He said: “We’re not in danger. We’re not even halfway through the season.
“I know people don’t want to hear this but it does sometimes take time. It’s always about results but I know if we play like this we’ll get results much more often than we have.
“I’m in a positive place with our group, I’m really happy to see so many of them commit to the things we want, to play with confidence and belief and now we need to continue on this path and even get better.”