James McKenna, spokesman for the Spirit of Shankly supporters' group, said the decision left him bemused.
The Spirit of Shankly group, which organised the protest, had been hoping thousands of fans would attend.
Yorkshireman Storton, signed by Bill Shankly from Tranmere, was part of the Reds' Uefa Cup-winning squad in 1973.
Paul Martin of fans' union Spirit of Shankly said supporters always wanted the club to remain at Anfield.
Dion McLeish was arrested at Dens Park stadium on Wednesday night after widespread disturbances in the Bob Shankly stand.
Supporter groups Spirit of Shankly and Keeping Everton In Our City launched the plans for the Football Quarter at the Museum of Liverpool earlier.
Liverpool built the Shankly Gates at Anfield in his memory and in 1998 Preston North End named their new stand the Bill Shankly Kop.
The Spirit of Shankly fans' group, who are committed to the removal of American co-owners Hicks Sr and George Gillett, had called for Hicks Jr to resign.
As a player for Preston North End Shankly's peak years coincided with the Second World War, and he lost several years of his career to the conflict.
Fans group Spirit of Shankly called the increases inflation busting.
Last October, several hundred Liverpool fans staged a protest march organised by the Spirit of Shankly group against the owners ahead of their Premier League clash against Manchester United.
Shankly's first task was to rebuild the team, the tide turned with two signings in the summer of 1961, "The turning point and the beginning of the whole affair was the signing of Ian St John and Ron Yeats, " Bill Shankly told the BBC after his retirement.
One of Shankly's greatest achievements was turning a defeat in to victory, famously after Liverpool had lost to Arsenal in the 1971 FA Cup Final, Shankly addressed thousands of fans who, despite the heartbreak of losing at Wembley, had gathered the day after the final at Liverpool's St George's Hall.
After Liverpool's 3-0 demolition of Newcastle United in the 1974 FA Cup Final supporters bowed at Shankly's feet on the Wembley turf, "These are the people, who came on the field and bowed down, these are the people I'm pleased for, more than anybody else, more than myself, " Shankly said after the match.
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