The apology on behalf of a health board to two pensioners came minutes after the First Minister and the Health Secretary accused Labour health spokeswoman Jackie Baillie of "scaremongering" over "untrue" blanket shortage stories.
The First Minister later met with 92-year-old Helen McBeth and Jack Barr, 65, who told him they had only sheets and a towel to keep them warm in the Royal Alexandra Hospital in Paisley.
Last week the Evening Times reported how a patient at the hospital was given a pillow slip to dry herself with after being told there were no towels.
In Holyrood, Labour leader Johann Lamont raised the cases of Mrs McBeth and Mr Barr, who spent days in the hospital with Mr Barr being told by apologetic nurses blankets were like "gold dust".
Mr Barr said: "After my operation I had just a sheet and my beach towel round me. When my daughter asked again about a blanket the nurse said, 'sorry they're like gold dust'. This shouldn't happen."
After hearing Mr Salmond state that the stories were not true, Mr Barr said: "We are not telling lies, I'm not happy about that. The First Minister is taking it on board and they said they will deal with it."
Mrs McBeth said: "The nursing staff were brilliant but during the night I was freezing and I got up and I asked for a blanket, but I was told 'sorry we haven't got any to give you'.
"I went back to bed with my dressing gown three sheets and a towel I had with me."
The Scottish Government and the health board said there was not a shortage of blankets but a problem in the supply from the warehouse to the hospital.
A spokesman said: "Both the First Minister and Health Secretary apologised on behalf of the health service for their individual experience and the lack of blankets."
"Greater Glasgow and Clyde Health Board have made it clear there is no truth in claims that there is a shortage of linen at the Royal Alexanda hospital, but have acknowledged that there were internal operational issues at the hospital relating to the supply of linen from the hospital's in-house linen store to the wards."
Ms Lamont said Mr Salmond "is in denial". She added: "It is easy to dismiss another politician but we have to listen to people in the community.
"They have given a commitment to look into it. The test now is in how they act."
A spokeswoman for NHS Greater Glasgow and Clyde said: "We want to apologise to any of our patients who feel that the linen, towelling or blanket provision was not adequate.
"There is no question of a shortage of supply or funding to purchase linen.
"Over the past year alone £1.2million has been invested in new and replacement linen for our hospitals."
stewart. paterson@heraldand times.co.uk