Wilson said that the Owls firstly offered £75,000; then the second bid was £75,000 plus a further £25,000 if Wednesday get promotion, plus Peacock.
The Dons manager, a former Wednesday boss and player, is unhappy that news of his old club's interest leaked out, and decided to speak out.
"It looks to me like somebody has tried to unsettle the player," he said. "The source was not us.
"We're not prepared to let Clive go, not for the derisory amounts that Wednesday offered.
He's an integral part of what we are building here for the future.
"He's suspended for four games and we miss him. He's a tremendous player.
"I could have had an unhappy player on my hands. But we have been straight with him; we have kept him informed. That's the way we work here."
Sheffield Wednesday's communications manager Steve Chu said: "I can confirm that we have made a bid for Clive Platt. However, we have been told by the MK Dons that the player is not for sale."
Peacock has played in the Owls' first three games of the season and worked under Wilson at Bristol City.
Wilson said the bids for Platt were made last week.
Wednesday signed striker David Graham for £350,000 from Wigan on Thursday but may see the 6ft 4ins Platt as someone who can add physical presence and aerial power to their squad.
Paul Sturrock is not likely to shed any light on the affair or on Wilson's inference that it was someone at Hillsborough who sought to unsettle Platt: the Owls boss is a firm believer in discretion when it comes to transfer affairs, and only confirms names to the media when a deal has been done.
Striker matters will be on Sturrock's mind tomorrow when triallist Steve Claridge plays for the Reserves against Walsall at Hillsborough (7pm) in a game that will decide whether or not the Owls make him an offer.
Sturrock will also assess several other players who have a chance to stake claims for places in Saturday's match at Ipswich.
On Claridge, he said: "We'll decide on what we see on Tuesday. His personality would be a great thing to the club.
"I'm led to believe by everybody I talk to, and by what I saw in training last week, that he's still got 'legs.' I do know that he'd be there in the box. That's the experience we need."
Sturrock is also beginning to gear up for Saturday's tough test at Portman Road. "This is a big, big game for us. This is the first of the real ones. Stoke had 10 men, Hull had come up a league, Southampton had just been a Premiership team. The next ones are real games where we play hardened Championship teams."