The local youngsters have not had their contracts renewed after failing to make the first-team squad this season.
Stockford, in particular, featured heavily in pre-season under ex-Blues boss Steve Cotterill.
Yet the former Priory School pupil never made the breakthrough.
They join fellow first-year professional Carl Walshe in leaving Fratton Park.
It is a massive disappointment to the home-grown duo, who have long been part of the Blues’ set-up.
The 19-year-olds both graduated from the club’s academy in the summer of 2011 and were rewarded with 12-month deals.
They appeared in the opening pre-season friendly victory over the Hawks.
Stockford also turned out as a substitute against Chelsea before taking his place on the pre-season tour to America.
Tallack and Stockford later started the rearranged friendly against Real Betis in August.
However, despite Pompey possessing the smallest squad in the Football League, they never even made the bench this season.
Tallack, from Waterlooville, went on loan to Dorchester for several months earlier in the campaign.
The pacy right-back ended the season on loan at Poole Town.
He made 11 appearances for the Southern League division one south & west club and was part of the team which lost 3-1 to Gosport in the play-off final on Monday night.
Meanwhile, Stockford spent time with Salisbury City during the season. He returned to Fratton Park when Cotterill was replaced by Michael Appleton.
However, the first-team call-up never came.
Instead, he joined AFC Totton in March and helped them reach the Southern League premier division play-off final.
Fratton team-mate Walshe has also been shown the door.
The Irish striker arrived from Home Farm in the summer of 2009.
He joined Frome Town on loan in February, making three appearances.