Noble was sounded out by the Football Association of Ireland earlier in his career because his grandparents are Irish but he turned them down as he wants to play for England.
"From my point of view, he made the right choice," said Pearce.
"He's a big part of this group and was disappointed to be watching the game on Friday through suspension."
Noble lobbed home the first in the 10th minute after Darren Randolph fumbled. The he beat the goalkeeper with a crisper finish seven minutes later.
James Milner sealed the win in the 26th minute when his effort was deflected in off Darren O'Dea, maintaining England's 100% record in Group 3.
"I was delighted with the performance," Pearce said. "They were sensational.
"Whenever you take the field against an Irish team and you are wearing the Three Lions, you know what you are going to get from the opposition.
"We matched them for endeavour and had the cutting edge."