Canada went behind to a stunning goal directly from a corner in the fourth minute, but rallied to equalise on the stroke of half-time before completing the turnaround early in the second half.
"I said at the end, 'It can be the making of us,'" Priestman told a press conference. "It's tough. We wobbled in the first half, our bravery wasn't there and I felt we played a little bit scared.
"I reminded them that we're Olympic champions and that we've got to take a step forward and be brave and get after this, and it's not going to be easy.
"The character, the quality, the experience that came about in the second half, that's the type of performance that we need."
Canada looked nothing like Olympic champions in their 0-0 draw with Nigeria and for the first half on Wednesday. When Ireland captain Katie McCabe curled in a brilliant corner kick early on, Canada's chances felt as funereal as the sodden weather at Perth Rectangular Stadium.
But an own goal by Ireland midfielder Megan Connolly evened things up just before half-time, then Adriana Leon scored in the 53rd minute, and the seventh-ranked Canadians thoroughly dominated until the final whistle.
"When we play brave, we can be unstoppable," Priestman added.
"I think it took it took a rocket in the first half and half time to really make us believe that and I think when this team plays with bravery and belief, we can do what we did in that second half."
The British coach also made some key changes at half-time, bringing on 40-year-old Christine Sinclair and Sophie Schmidt, who have close to 600 caps between them.
"Listen, Sophie Schmidt, Christine Sinclair, I thought their quality when we really needed it, they just allowed us to keep the ball in building," Priestman said.
"It was a big part of the game plan. My explanation for the selection was exactly that, 'You can be the reason that we win,' to come in and bring that quality when we really need it."
Sinclair, who has the most international goals in history with 190, gingerly limped off the pitch at the final whistle and Priestman confirmed her captain was being tested for an injury, but she did not know the details.
A goal in this tournament would make Sinclair the first player to score at six World Cups.
Canada play Australia in their final Group B game on Monday in Melbourne.
