Palace twice came from behind to earn a Premier League draw at the London Stadium, with Gallagher scoring the first goals of Vieira’s tenure.
Pablo Fornals and Michail Antonio had put West Ham ahead on two occasions as their 100 per cent start to the campaign ended due to Gallagher’s strikes.
Vieira, who has admitted the club are keen to add a striker to their ranks before Tuesday’s transfer deadline, at least has faith that the England Under-21s international can weigh in throughout the season.
“He has got the ability to remain calm inside the box,” he said of Gallagher.
“He is a really good finisher, has got a lot of energy and works really hard for the team.
“When he is in that kind of situation he will score goals for us.
“I was really pleased with the two goals we scored of course but I never had any doubt about us scoring goals, it was just a matter of time. We were unlucky the last couple of times we played.
“I think it was a well-deserved point. We played well, especially in the second half.
“I was really pleased with the character we showed today and we have to build up from that performance.”
Additional reporting by PA.