The former Iceland manager handed a first start to Leicester City’s McAteer and he rewarded the faith shown by his manager by netting the opening goal in Dublin.
Hallgrimsson said the 23-year-old put in a “really good performance” on his maiden international start.
“He showed a lot of confidence, took players on and got the goal as a reward,” he added.
“I’m really happy for him.”
The Republic are back in action on Tuesday away to Luxembourg in their final friendly before the start of World Cup qualifying, when the Irish will face Portugal, Hungary and Armenia.
Hallgrimsson’s side are now unbeaten in three matches and he wants his team to carry that momentum into Tuesday’s friendly before their World Cup bid begins.
“The big thing from this game is we can play top teams,” he added.
“We are disappointed not to win the game tonight, and at times we made them look an average team.
“I’m mostly happy with how we dealt with their possession game, we limited their goalscoring chances and when you play good teams that’s an absolute priority.
“If you look at where we are at the moment, and what run they are on I think we should be happy with the performance of the players tonight.”