Sherwood was strongly linked with the vacancy at The Hawthorns after departing Tottenham at the end of the 2013-14 Premier League season.
However, West Brom announced on Saturday that Everton academy boss Irvine, a former manager at Preston North End and Sheffield Wednesday, had been chosen to succeed Pepe Mel.
Sherwood has subsequently confirmed that he did hold talks with West Brom, but opted to turn the club down.
In an interview with talkSPORT, he said: "I went to speak to the chairman and the board there a couple of times and was happy with how the discussions were going.
"I was offered the job before we started to negotiate. It just wasn't right for me in the end, so I decided to give it a miss.
"It is a fantastic club and it looked on the outside like it might be a perfect fit for me, but unfortunately we couldn't agree for me to move forward.
"I was pleased with most things we were talking about and it was a good opportunity for me to get back in very, very quickly. But, in the end, I decided when we prolonged the discussions that it wasn't right for me.
"I wish them all the best and Alan in particular, someone I played with a long time ago at Blackburn."
Keith Downing and Dean Kiely have been kept on by West Brom as part of Irvine's coaching team, but Sherwood was keen to bring in his own backroom staff had he been appointed.
"I don't know Keith or Dean very well and I've got nothing against them. I think it is important you take your own men in and I was looking to bring in a couple of guys who I trust and who I know," he added.
"When you go into a club you haven't got time to try and train someone to your own thinking.
"There were just a couple of ingredients missing which made me decide I wouldn't take the gamble on it."
