The management duo were half way through their third season at Netherdale - currently sitting second top of the First Division.
But a lack of financial backing from the club"s committee or any long-term assurances led to last Wednesday"s decision.
They will be replaced by former Selkirk coach Fraser Lothian, assisted by his Yarrow Park sidekick Ally McCulloch, Kelso boss Gary Fraser and former Vale coach Stuart Robertson.
Templeton told the Border Telegraph: 'Ever since we started we"ve been unable to give our players anything for turning out week after week while other clubs have been spending freely.
'We knew the financial position when we took the job but the club has money now and we wanted some of it to reward the boys we"ve got and try to bring in some other players.
'The committee don"t want us to spend money, or for us to be at the club next season. We didn"t feel we had any other option than to quit.'
The Border Telegraph understands that only two of the club"s committee were backing Templeton and Hancock to be in charge next season. And replacements had already been discussed in the boardroom.
Simon Gillie resigned from the vice-chair post earlier in the season. He told us: 'I think it"s terrible the way Bryan and Derek have been treated. They took us from being bottom of the league with a huge wage bill to a force to be reckoned with again, and without spending a penny.
'They should have been given the chance to spend on bringing a couple of players in - the Fairydean are in with a good chance of going up.'
Current Spartans coach Mark Lamb, who worked with Templeton and Hancock at the start of the season, was believed to be the popular choice amongst some of the players.
Fairydean chairman Jos Ritchie said: 'I was surprised when Bryan and Derek resigned. The club is in a good financial order for the first time in years and we were looking at how we could take the club forward. None of us expected for them to resign.
'We should thank Bryan and Derek for everything they"ve done over the past two or three seasons. We wouldn"t be where we are just now without them.'
Gala Fairydean are due to travel to face Gretna on January 10.