The south London club travel to rivals Brighton and Hove Albion on Wednesday in 12th place in the standings but only three points above the relegation zone.
A narrow defeat by champions Manchester City last weekend continued Palace's winless run and Vieira, for the first time since taking over in 2021, is coming under pressure.
But the former Arsenal midfielder says that while results need to improve, he retains faith in his ability and his squad.
"Season after season, if you do well in the first season, people expect you to keep improving," he told reporters.
"It is not always the case. It is important to understand where we are, what we want to achieve and the direction we want to go in. It will take time to be consistent.
"That is why it is important for us to remain calm and to keep working and keep believing in the players we have in the building. I'm convinced with the way we are working."
Clashes with Brighton are always feisty contests and the fact that Brighton are pushing for a European qualification spot means this fixture has even more on the line than usual.
"Every game is important, but of course, this is the special one because it is a derby," Vieira said. "We know how much it means to the football club and the fans."
Palace, who will be missing Will Hughes (27) and James McArthur (35) for the trip to the south coast, have gone three league games without scoring and Vieira knows their attack must start firing soon to avoid falling further into danger.
"You can always read the stats in a way that suits you. What is clear is that we are not scoring enough goals. That is a fact. We have to play better and create more chances," Vieira said.
"It is about working a lot in the last third, about having people inside the box, about the quality of our passing.
"It's about changing our mindset to be more ruthless in front of goal."
