Rob Howley will lead Wales on the three-Test tour and Jones insists there is a collective duty to ensure the Dragons continue to roar.
"It's a reciprocal thing now Warren is out and we have to work together," said the 2009 Lion.
"When Sam (Warburton) was injured in the Six Nations all the players stepped up to the mark and backed the management. Now Warren is out of the tour the management will step in.
"I'm sure Howls (Howley) will do a good job, but it's also down to the players to step up and help them."
Jones still reckons Wales have a golden opportunity to secure a southern hemisphere scalp against the Lions next opponents despite Gatland's absence.
But the second-row insists Wales cannot afford to make the same mistakes as following the 2008 Grand Slam and must continue to build on this season's progress.
He added: "In 2008, it was all change and all new. Gats came in and bang we won the Grand Slam but we didn't back it up.
"But there's a big opportunity now with the core of the side not only from the Grand Slam but the World Cup as well.
"We have that consistency and if we can keep it together for a third time in the summer then it bodes very well for the future. We can do really well down there."