The pair clashed after Deeney was dropped for the 4-0 defeat at Tottenham last Saturday.
Hornets manager Mazzarri insists there is no issue now with Deeney set to start against Swansea today, but warned he will retain the final decision on team selection.
“There was no problem at all,” said Mazzarri. “I spoke to him and everything is perfect and was never really a problem.
“As a manager I have a clear relationship with all my players.
“It’s based on mutual respect and the best for the team. He is loved by the fans. But no player or individual will be above me.
Walter Mazzarri has cleared the air with Troy Deeney Premier League predicted table: April update Fri, April 14, 2017
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“He is the captain and after the manager he must provide an example to everyone. In a ship the captain is last to leave – and it must be same as the captain on the pitch.
“They need to understand the manager takes the decisions and players have to do their best on the pitch.
“There were times when I’ve done the same with other players, including Edinson Cavani (at Napoli).”
Swansea manager Paul Clement says his players can handle the pressure of a relegation dogfight.
Five points clear of the bottom three at the start of March, a five-game winless run has seen the Welsh club drop back into danger. They are now two points adrift of safety.
Clement wants his experienced stars to use their big-game mentality to help the team move away from trouble.
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Paul Clement has backed Swansea to beat the drop
Fernando Llorente has a World Cup winners’ medal with Spain, Federico Fernandez starred for Argentina at the 2014 World Cup and Gylfi Sigurdsson was in the Iceland team that shocked the world by reaching the quarter-finals of Euro 2016.
“We have a whole wide range of different players that have had different experiences,” said Swansea head coach Clement. “Some players have played at big clubs, Llorente is an example of that. Tottenham are a big club, some of our players have played for them, recently.
“Llorente, Sigurdsson and Fernandez, they are players who know what it’s like to play in big games.
“We have young payers who are new to this with very few Premier League games. What you hope from the experienced players, and they have been very good, is that they try to galvanise the dressing room and give their advice and experience to the younger ones and help them.”