Former Dundee United manager Houston, pictured, has been in charge at the Falkirk Stadium since June 2014 and during that time he has led them to a Scottish Cup final as well as the last stage of the Premiership play-offs, where they lost to Kilmarnock.
This season started well enough with a perfect four wins from their Betfred Cup group, even leading to talk of a return to Hearts for Houston as the Tynecastle club searched for a replacement for Ian Cathro.
However, no wins in seven league games sees Falkirk, who finished second to Hibs last season and Rangers the year before, sit second bottom, just one point above Brechin.
Saturday’s 2-0 home defeat by Livingston was the last straw with the club announcing last night that it had come to a mutual agreement for Houston, McDonaugh and Maybury to leave with immediate effect.
Technical director Alex Smith will take charge of the first team on an interim basis, with senior squad players Mark Kerr and Lee Miller helping out alongside academy director Michael McArdle.
A club spokesperson said: “We want to thank Peter, James and Alan for the enormous amount of work they have put in to improving the football department over the past three years.
“Under their stewardship Falkirk have enjoyed some memorable occasions, including the 2015 Scottish Cup final and two successive runners-up finishes in the Ladbrokes Championship.
“The board will take time to recruit the right management team to lead the club forward.”
Houston thanked the players, his backroom staff, the board and the fans for their support and added: “We are disappointed with the start to the season and the board and I have come to a mutual agreement that to get the club moving again it is best that someone fresh is brought in.
“It has been a decent three or so years; there have been some real highlights, including reaching the Scottish Cup final and finishing second, but we just fell short of the goals we all hoped we could achieve. It wasn’t down to lack of effort and I’ve got to thank the players for all they have put in.”
Houston added: ““I must also mention the supporters. It has been a wee bit rough recently, but through the last three years they have given great support to the club. The fans have been magnificent.”
“Finally, I’d just like to wish the club the very best moving forward. I hope whoever comes in can give the club the success it deserves and that we have been striving for over the last number of years.”
The Chair of the club Margaret Lang said: “We are all extremely disappointed that we haven’t been able to progress forward this season and as a result we have come to a mutual agreement with Peter, James and Alan.”
“I have nothing but admiration for the job all three have done for our club and wish them the very best in the next chapters of their careers.”
“We will now work to recruit the best possible management team to get the club back to winning matches, climbing the Championship table and moving towards the Premiership.”
Former Dundee manager Paul Hartley is likely to be on the club’s list of possible candidates to replace Houston, while a couple of former Falkirk managers – John Hughes and Steven Pressley – could also be in the frame.