The on-loan midfielder’s brace earned Palace a draw at West Ham.
Palace twice came from behind to earn a 2-2 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.”
West Ham boss David Moyes pointed to what he considered to be a poor playing surface at the London Stadium as a reason his side struggled, admitting it is something he has had concerns over since his arrival at West Ham.
“We didn’t pass the ball as well as we did the other night (a 4-1 home win over Leicester),” he said.
“Our rhythm and passing was not as good the other day. Several reasons for that. It was made a bit difficult.
“I’ve got to say the pitch is very poor, the pitch at the London Stadium is really, really poor. It’s not an excuse because we played very well on it on Monday night.
“Today in the dry, a bit of heat it is not good. That didn’t help. You could probably see the amount of times the ball bounced over people’s heads and it was very high off the ground. I think we never really got a good enough rhythm in our play.
“I’ve not enjoyed the quality of the pitch at all, and I’ve known about it. Even the first game I wasn’t happy about it.
“It’s just not good enough, it is certainly below Premier League standards at the moment.”