In a statement released on behalf of the St Mirren board, Gilmour and his colleagues have accepted they made a mistake in appointing veteran coach Tommy Craig as manager last summer.
Craig was promoted from his position as assistant after Saints decided not to renew the contract of their 2013 League Cup-winning manager Danny Lennon at the end of last season.
It proved a calamitous decision as Craig oversaw just three victories and suffered 13 defeats in his 19 matches before he was sacked in December with the club at the bottom of the table.
Former Scotland winger Teale was placed in charge until the end of the season, assisted by the club’s head of youth development David Longwell, but was unable to significantly reverse St Mirren’s fortunes on the pitch.
After nine successive years of top-flight football, their automatic relegation as the bottom-placed team was confirmed on Friday night by Motherwell’s 3-1 win over Kilmarnock.
“There is no getting away from the fact that this has been a difficult and disappointing season for everyone connected with St Mirren Football Club, culminating in what will be a 12th place finish and relegation to the Championship,” read the board’s statement.
“As a board of directors we have always made what we believed to be the best decisions for the good of the club. This season, unfortunately, we have got some of those decisions wrong, and we hold our hands up and accept responsibility.
“One of the reasons we all love football is that it moves on quickly and as a club we have to do the same and start the rebuilding process immediately. So rather than spend the next few months dealing with the recriminations we will look to the future and start this process from today.
“The first step on this road is the appointment of a new manager. We are now inviting applications from managers interested in managing this great club with first-class facilities and excellent young players.
“The board would like to place on record our thanks to both Gary Teale and David Longwell for taking over the reins after Tommy Craig’s departure and whilst the job of avoiding relegation proved to be a step too far their commitment, effort and endeavour has been there for all to see.
“We would expect Gary to put his name forward for the vacant manager’s position and we will duly consider his application along with all others we receive.”