Sam Allardyce's team went out of the UEFA Cup last week to Olympique Marseille at the Stade Velodrome, the scene of Newcastle's semi-final exit in the same competition in May 2004.
Elliott said, "They're disappointed after their exit. But they have a big carrot in front of them to get there again.
"European football was unheard of at Bolton at one point, but fair play to Sam and his backroom staff – they've been playing their way and it will be tough."
Elliott – set to make his fourth consecutive start – spent four years at Bolton before returning to St James's Park in the summer of 2001.
He said: "It's always nice to come up against your old club and friends – my time at Bolton was four of my best years.
"They always come up here and give us a battle. Sam Allardyce is fantastic as a manager, and he's not scared to try new things. If they work he will keep them and not ditch things.
"I enjoyed my time there, and a lot of that was down to him."
Elliott said, "They're disappointed after their exit. But they have a big carrot in front of them to get there again.
"European football was unheard of at Bolton at one point, but fair play to Sam and his backroom staff – they've been playing their way and it will be tough."
Elliott – set to make his fourth consecutive start – spent four years at Bolton before returning to St James's Park in the summer of 2001.
He said: "It's always nice to come up against your old club and friends – my time at Bolton was four of my best years.
"They always come up here and give us a battle. Sam Allardyce is fantastic as a manager, and he's not scared to try new things. If they work he will keep them and not ditch things.
"I enjoyed my time there, and a lot of that was down to him."