The Liverpool academy graduate attracted interest from a host of clubs, with 18-times Serie A champions Inter among his suitors.
Talks with the San Siro outfit reached an advanced stage, but Ince decided to stay closer to home, swapping Blackpool for Hull.
Livermore, who was on loan at the KC Stadium last season, walked away from a long-term contract at Tottenham and he respects the decision taken by Ince, though he only offered a wry smile when asked if he would have taken the same one.
"It's a great opportunity for him to come here and play Premier League football," Livermore, Hull's record signing, told Perform.
"He's got great talent and to share that here with us and progress would be great.
"I've had so many people when I made it apparent I wanted to join Hull saying, 'There's bigger clubs you could join'. At the end of the day, if a player is happy with where he wants to go, happy with the manager and has a good set of lads around him, that's what it's about.
"It's also about challenging yourself in life sometimes. If I wanted the easy option I could have stayed at Tottenham and seen the rest of my three or four years out that I had.
"For me, I wanted to be part of something and obviously help Hull City and me go in the right direction, which is up."
