"It's a lack of respect. He wants to play," Ferdinand's representative Jamie Moralee told BBC Sport after Hodgson brought Liverpool's Martin Kelly into the squad.
"Rio's very disappointed. He thought he had done enough. It's very difficult to accept. This is a player with 81 caps for his country. I don't know anyone who understands it. It's not been handled in the right way."
Chelsea centre-back Cahill was ruled out of the tournament, which starts on Friday, with his jaw fractured in two places after colliding with team-mate and goalkeeper Joe Hart during England's friendly against Belgium at the weekend.
Kelly, who made his international debut as a substitute in last month's friendly against Norway, was on the standby list.
Former England captain Ferdinand won his last cap against Switzerland in June 2011 but has had injury problems since.
When announcing his initial squad last month, Hodgson said it was a "footballing decision" to leave the 33-year-old out despite media reports that Ferdinand and fellow England international John Terry had fallen out.
Defender Terry, who is in the squad, will go on trial on July 9 charged with racially abusing Ferdinand's brother Anton, a Queens Park Rangers player. Terry has pleaded not guilty.
England begin their Euro campaign against France in Donetsk on June 11 before facing Sweden and tournament co-hosts Ukraine in Group D.
