The former England international made a surprise departure from the League Two outfit, whom he helped avoid relegation last season.
Beattie has been linked with various clubs only days after his resignation, but the 36-year-old was focused on thanking Stanley for giving him his first managerial chance.
"It is with a hugely heavy heart that I decided to end this journey," he told Sky Sports News.
"I can never fully repay the faith and backing I got from the players, my staff and of course the fans - who always gave me 100 per cent.
"I thank them from the bottom of my heart for granting me the opportunity and privilege to be part of your unique club."
Managerless Accrington managed to snatch a late victory against AFC Wimbledon just days after Beattie's departure.