Blackburn tried to sign Jones from Sunderland over the summer, but the Trinidad and Tobago international ended up joining Stoke in a £8million instead.
Allardyce told The Sun: “He was out of our price range.
“We would have loved him here and I spoke to Steve Bruce about it but unfortunately it wasn’t something we were able to do.
“He’s very powerful, a really good target man with Premier League experience.
“It’s difficult to find players like that and it’s not often you find one that a club is willing to let go.
“I was unable to do it. It’s frustrating but it’s the reality.”