Nine players - including Wilfried Zaha and Marc Guehi - have not travelled to Singapore and Australia, with the club suggesting that some players were not fit or did not meet entry requirements for the countries "when travel arrangements were made".
Vieira refused to discuss the players' COVID-19 vaccination status, with restrictions in place for both countries.
The Palace boss said: "It is not the ideal situation for a manager to have so many players behind.
"It is important to understand players have stayed behind for different reasons. We are not going to talk about the private situation of players and whether they are vaccinated or not. Some players stayed behind because they needed to have more training and play more games."
Palace are due to take on Manchester United in Melbourne on Tuesday (19.07.22) and Vieira is concerned that he is unable to have his full squad together.
He said: "It is difficult. It hasn't allowed us to play games together and work on a tactical basis together. It will take a couple of games before the team starts to gel."
Vieira wants to build on Palace's mid-table finish last season and is keen to add new faces to his team.
The French coach said: "What is important is to try and improve from last year in the way we want to play the game.
"One of the ways of doing that is to improve the squad. We are still short in the number of players we have. Hopefully we will make a couple of signings that will help us to be more ambitious."