Baggies fans watched their team survive in the Premier League by the skin of their teeth last year, avoiding the drop by only three points.
"It was not the campaign we hoped for or expected, and as the chairman of the football club, the buck stops with me," Peace is quoted as saying by the Daily Mail.
"The squad we assembled during the summer transfer window has not performed as consistently or as well as we would have hoped. We have been taking a long, hard look as to why this has proved to be the case, especially in terms of our player recruitment."
Chris Hughton and former Celtic boss Neil Lennon are two names that have been linked with the vacant managerial post at The Hawthorns.