The Brewers had lost their opening three games of the 2017-18 Championship season but got off the mark against the Blues, coming from behind to claim all three points at the Pirelli Stadium.
Following promotion to the second tier last season, Burton lost their first two games, but went on to survive in the division despite many having tipped them for relegation.
Irvine told Sky Sports News: "I think all the players were aware they needed to show a little bit more in the second half. The whole flow of the team was a bit better in the second half.
"I think the first points are always important. We had the same thing last season, we lost the first couple of games, but when you get those first points it gets you up and running."
Up next for Burton is an EFL Cup meeting away at Cardiff City on Tuesday night, before resuming their league programme with a home game against Sheffield Wednesday next Saturday.