Beck took over from former VS Rugby boss Alan Lewer but according to the club's chairman Russell Hands, the pair parted over money issues.
"It was a difference of opinion," said Hands to BBC Radio Cambridgeshire.
"We couldn't give him what he needed to do the job. Because of the financial restrictions we're under he found it very, very difficult. "
In the end John felt that he had got as far as he could and in the interests of both parties we decided to go our own ways."
Beck made 69 appearances for the Sky Blues between 1976 and 1978 scoring six times before he was sold to Fulham. His management career includes Cambridge United twice, Preston and Lincoln City.