Stoke was trumped by Birmingham for the former Manchester United striker.
Pulis told the Sentinel: “Steve Bruce has signed a good player.
“But unfortunately there was no way in a million years he was ever coming to Stoke from Portsmouth.
“I’ve got a great relationship with Harry Redknapp down at Pompey and it’s well known he’s been a big help to us on deals such as Andy Griffin’s.
“We’ve brought in some very good players on loan this season, but there’s a limit to what we can do.”