"I would have loved Phil Neville at this football club - I would seriously have loved it," said Allardyce.
"And I'm sure if I had spoken to Phil Neville he would have loved to have come here, if we'd got in before Everton.
"I'm not saying that, if we were competing with Everton we'd have got him because, in the end, we couldn't have afforded it - not just the fee but the contract too.
"And for me that's my heartache. It's something we've always had to live with but it's still heartbreaking."
Allardyce made tentative enquiries but soon discovered, to his dismay, that he was out of his league.
"It's times like this when you really feel gutted - when a player like that, who is just down the road, wants to leave Manchester United and you know he can contribute so much and you can't compete financially," he said.
"We made the enquiry but couldn't have gone much further.
"For us, that sort of signing would have been a major benefit for a few years. But it wasn't to be."