The news that Irvine would be coming in as Pepe Mel's successor on a 12-month rolling deal has drawn a negative response from some Baggies fans, and there has been talk of an organised fans protest against the appointment.
Supporters have been crtical of the coaching credentials of Irvine, who has not held a senior management position since early 2011 and never one in the Premier League.
Peace told the Birmingham Mail: "People have their say but we have to make the right decision for the football club and not be swayed by what other people think.
"If you ask a lot of people who they'd have in the job they'd be split anyway.
"You can't always make the easy decisions. You have to make the right decisions.
"As a board we made a unanimous decision that we think is right for this football club. We now have to try and get players in and get people behind us.
"We think we can give ourselves a good chance of having a good season. Alan speaks well, his philosophies are good and we are confident people will buy into that. We have made the right decision for the club - we really do believe that."
Peace says the board regarded Irvine the best option after assessing the 55-year-old Scot against former Tottenham boss Tim Sherwood, who has claimed he was offered the job but turned it down.
Peace said: "We went through a lengthy interview process. We had about 40-odd people, shortlisted to about seven, went down to a shorter shortlist and the more you see of people, the more you get to know them, the more you get more impressed or the less you're impressed.
"Alan came through that process very strongly and ended up as our first choice. You might say that it was a difficult one given the reaction but we've tried to make the right decision from the club's point of view.
"We have a coaching ethic here. We feel that he fits the bill for us. We ended up with two very good candidates (Irvine and Sherwood) and when you look at them side-by-side the whole board went with Alan. It was unanimous."