The Baggies were made aware the striker had a clause in his contract allowing him to speak with other clubs offering above £3m – they bid £1 above that figure.
It left Latics' hands tied, and Ellington claimed on his arrival at The Hawthorns that he was surprised negotiations hadn't gone better at Wigan.
But Whelan is fuming at the remarks and takes the view it was the player's advisors who pushed the move through.
He told the Evening Post: "I have read the reports claiming Nathan's move to West Brom came about as we didn't offer him enough money to stay.
"That is utter nonsense, in fact the deal we offered Nathan was actually more money than he has ended up getting at Albion.
"In my opinion, this move has been engineered by his representative.
"The lad himself was crying when he said goodbye to me, he obviously didn't want to move."
Ellington had a year to run on his Wigan contract and two offers were made to him in the close season to extend his stay.
The final round of negotiations took place a week ago, and the following day, West Brom made their move.
Paul Jewell echoed Whelan's words, saying he wanted to keep Ellington at the club following his haul of 24 goals last season.
He said: "I was disappointed to lose him because he was our top scorer.
"Whether it was his advisor I don't know, but I'm not convinced he wanted to go. We made him what we thought was a very good offer to stay."
Ellington played 45 minutes for West Brom's Reserves against Aston Villa last night, with boss Bryan Robson keen for him to get some game time ahead of Saturday's Premiership clash with Portsmouth.
He should be reunited with his former colleagues next month when Latics visit the Baggies on September 10.
Latics have just a fortnight to find a replacement as the transfer window shuts for four months on August 31.
The striker they want is Norwich City's Dean Ashton and Jewell has a £7m kitty to try to tempt the Canaries to sell.
Ashton showed his Premiership qualities when he scored seven goals in 16 appearances for the East Anglian club in the second half of last season.