Johnson said the approach from Elland Road last week had given Barnsley “no decision to make”, with the League One club valuing their top scorer at over £1m.
Leeds’ offer for 25-year-old Winnall, who has scored 16 times for Barnsley this season, came with the January transfer deadline approaching and head coach Steve Evans increasingly anxious to add a striker to his squad.
United declined to return with an improved offer after their £300,000 bid was turned down flat.
Johnson said: “The bid certainly wasn’t acceptable. I don’t think even Sam thought it was acceptable if he was being honest. There’s no decision to make which means he cracks on and is happy. He was always happy here.”
Evans was critical of Barnsley’s reaction to United’s bid and frustrated that news of it was made public.
“There’s been some insulting comments come out of South Yorkshire about our bid,” he said. “We thought it was in confidence. Nothing to do with the player, he’s a decent player, but I’m not going to talk about him any more. We’ll not be going back for him.”