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Santa Cruz remains sidelined with a knee injury which has kept him out for two months and ensures he will miss Sunday's Premier League clash at Chelsea.
But the former Bayern Munich star has frustrated Allardyce by using his time off to focus more on talking up a potential close-season transfer than getting fit to play for Rovers.
Manchester City, Liverpool and Arsenal have all been linked with Santa Cruz and this week he went on radio in Paraguay to reiterate his desire to leave.
"He has become a little bit underhand. These kind of remarks always sneak out where we cannot control the situation. It has happened too many times for it not to be him and is disappointing," Allardyce said.
"That is life today but Roque should really concentrate on getting himself fit and playing football for Blackburn, never mind talking about where his future may lie.
"Without his fitness and his capability of producing more than last season, he will perhaps struggle to get the move he is looking for."
While Allardyce claims to have a good relationship with Santa Cruz, he has no intention of letting his star player leave unless the transfer fee matches Blackburn's valuation, which is thought to be around £15 million.
"I have always got on with Roque extremely well and explained the situation to him as it lay in January," Allardyce said.
"If someone meets the value, he is gone. It is that simple. It is a shame he has not been fitter because he is a terrific player.
"The fans will always take a dim view of someone who openly says he wants to leave. I understand that, so we will have to wait and see what happens."
