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.”
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?