Byrne, who returned to Wales in the summer after a stint with French side Clermont Auvergne, has been ruled out for three months after undergoing shoulder surgery.
The full-back has featured four times for Dragons so far in the GUINNESS PRO12 this season, including the region's only win of the season against Benetton Treviso.
However, while Jones knows his captain will be sorely missed he is focused on lifting the Dragons up from tenth position - starting with a win at home to Munster on Friday.
"When Lee plays for us we are a different team. He has been outstanding for us in terms of his leadership and playing ability, he can do things that not a lot of people can do," he told the South Wales Argus.
"You'd be surprised what a good full-back can do to a team and he will be missed but we need to get on with it and move forward. We have plenty of options to go there.
"The last eight weeks have been horrific. We are building our game back up again and as the players come back from injury we expect to improve.
"We have been working towards this Munster fixture for three weeks, trying to get people ready for selection and trying to generate some momentum to kickstart our Pro12 campaign."
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