The Dutch side's technical director Martin van Geel said: "Henk spoke with Chelsea a week last Thursday. The following Tuesday Henk approached the board and said he wanted to go to Chelsea.
"Henk presented it to us as a fact and we didn't have any choice.
"We didn't want to work with a coach who had his mind at Chelsea.
"Things should have been done differently. I don't want to say more."
And Van Geel hinted Ten Cate's actions could have affected the team as it unsettled the dressing room.
Van Geel added: "You can't prove it had an influence on results but it was the talk in the dressing room."