The Ghanaian has not scored in 36 games for the Eagles, and missed a brilliant opportunity to give his side a 2-0 lead against Brighton Hove and Albion on Monday night.
That miss proved costly for his side with Neal Maupay scoring a 95th minute equaliser for Brighton to deny Palace all three points in the derby.
Ayew has featured in all six Premier League games under new manager Vieira whose side have won just once, drawn three and lost two.
What Patrick Vieira has said
Crystal Palace manager Patrick Vieira said: “I think what is really important for Jordan is that, as a manager and as a football club, we believe in his ability.
“He needs to know that we have the total belief that he can score goals and he has got the support of everyone at the football club.
“There is no question or doubt about what he is capable of achieving, saying that it is also one part of the game he needs to improve.
“Because we want him to score more goals and how can we do that, we have to continue to work on his confidence in training and put him in a situation that he will likely face in real game time.
“With the support we will give him he will score goals, I don’t have any doubts. I just want him to improve and be better than he was every single day.
“As a player it is important for him to keep working hard and keep going the way he has been doing so far for himself and his team-mates.”
Vieira also had some praise for forward Wilfred Zaha who has scored 49 goals for the club, and put his side ahead against Brighton on Monday night.
He added: “Wilf is Wilf and there is no doubt that he is very important for this club and he has a special connection to the people here.
“Hopefully he can get the 50th goal and help us all to have a very special season together but the Premier League is tough, every game is a battle for him and to do this shows his quality.”
Five facts about Jordan Ayew
- He is the son of former Ghana captain Abedi Pele and brother to former Swansea City striker Andre Ayew.
- Ayew started his playing career with Olympic Marseille where he progressed and made 111 appearances for the first team and scoring 14 goals in return.
- Ayew has been capped 68 times for Ghana and has 18 goals to show for it.
- Ayew joined Crystal Palace on loan from Swansea City on transfer deadline in 2019, before signing on permanently a season later.
- He won the Crystal Palace Player of the Year and Goal of the Season awards for his contribution during the 2019/2020 season.