McAuley broke the deadlock with a second-half header before substitute Niall McGinn wrapped up the Green and White Army's maiden win at a European Championship finals with an injury-time strike.
"We had a point to prove to ourselves," McAuley told ITV.
"It's pleasing. We've a tough game ahead but we are delighted. Lots of people were saying we wouldn't get a point.
"We thought we let ourselves down with the intensity we played at [against Poland]. We just didn't get that right. We weren't at it against Poland, not to your standards.
"The lads will take confidence from this because we had been written off."
McAuley's strike which got Michael O'Neill's men up and running against Ukraine was Northern Ireland's first strike at the Euros for 30 years and the defender says it was “special” to be the man to end his country's long wait for a goal at a showpiece competition.
"It's special. It will sink in over the next few days," he said of the goal.
"But it was the team performance that was pleasing, the reaction after getting beaten by Poland and now we’ve got a tough game to look forward to now.
"We've given ourselves something to play for and that's what we wanted."