Hull are looking forward to a first European campaign after finishing as FA Cup runners-up to Arsenal last season.
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And with several of his team-mates boasting similar experience, the midfielder is confident Hull can make a positive impression.
"We'll go into this not fearing anyone," Livermore told the Hull Daily Mail.
"We had that mentality last season and it served us well. There's also a good nucleus of this squad who have been there before.
"There's myself and Tom (Huddlestone), who played a lot of games in Europe with Tottenham, and then there's Curtis Davies, Allan McGregor and Nikica Jelavic who have been there before with past clubs.
"The spine of our team has played a lot of games in Europe so I don't see why we can't have a good run."
Livermore agreed a permanent move to Hull earlier this week, following a successful loan spell, and the Yorkshire club are expected to complete further signings before entering the Europa League's third qualifying round.
"People will say it can be a hindrance to your form and all the rest of it but we've got a young, fit squad who are well-equipped for it," Livermore added.
"I'm sure the manager will bring one or two more in and, with the squad that was already here, I'm sure we'll be okay."