Albion built on last weekend's surprise success at Tottenham by comfortably beating Burnley in the Premier League at The Hawthorns on Sunday after the midweek League Cup defeat of Hull City.
Saido Berahino bagged a brace to take his tally for the season to five in all competitions, while former Burnley transfer target Craig Dawson broke his duck for the club and Graham Dorrans rounded things off with a well-taken strike.
"I said a few weeks ago I felt we were getting closer to where we need to be," said Albion head coach Irvine on Sky Sports.
"We've still got lots to do but it's been a great week and the players got their reward for the work they've done.
"I've been happy with the way the lads have worked from day one, I believe they will continue to improve but I know how hard it's going to be.
"We won't get carried away, it's a good start but we have to build on that."
Berahino claimed his first league goal a year ago to the day in a 2-1 win at Old Trafford and epitomised the work ethic in the camp ahead of upcoming games against Liverpool and Manchester United.
"It's been a great week," said the England Under-21 international.
"We've stuck together during this period and the results are now paying off but we're not going get carried away.
"We're going to have to focus now on Liverpool away and make sure we get something there."
