Jones underwent an operation last week having struggled with niggling problems in the same shoulder that was rebuilt after the Lions tour in 2005.
Any hopes Wales had of Jones being available for the World Cup were dashed when the specialist advised he would risk long-term damage by playing at the tournament.
Jones explained: "I need to make sure it's right before I play and that means missing out on the World Cup.
"It's obviously bitterly disappointing but at the age of 26 it would be completely the wrong decision to try to rush myself back to fitness with a high risk that something could go wrong.
"I can't express how gutted I am to miss out but it means I will be able to get back to full fitness and turn out and captain the Ospreys next season and ensure I'm still around when it's time for the next one."
Dallaglio could empathise with Jones' plight after being forced to miss the bulk of successive Lions tours with knee and then ankle injuries.
The England international said: "The World Cup is a stage every player wants to play on. For any player to miss out on that because of injury, regardless of their nationality, is very unfortunate.
"You feel enormous sympathy for him given he would have been in all probability a very important part of Wales' plans. It is a shame and I feel sorry for him."
Dallaglio's words are an indication of how highly Jones is regarded, not only in the Wales camp but on the world stage.
A dynamic loose-forward, Jones burst onto the Test scene in Wales' 2005 Grand Slam campaign and shone on the Lions tour of New Zealand after earning a late call-up.
He missed the majority of the 2005-06 season after undergoing surgery but returned to action last season and established himself again as a key part of Wales' World Cup plans.