The 22-year-old left BVB for Bayern in the summer of 2013 in a deal worth €37 million (£30m), causing uproar among Dortmund fans.
Gotze has been given a hostile reception on his returns to Signal Iduna Park since then but Watzke feels the Germany international, whose goal won the World Cup final this summer, does not deserve such a welcome.
"To be honest, I thought it was not correct when our fans all jeered and whistled Mario during the German Supercup," Watzke told Der Westen.
"I realise that the circumstances surrounding his transfer to Bayern were quite special but, when you look at it from a neutral point of view, you could say that he came through the ranks of the BVB youth academy, played for Dortmund for quite a few years and earned us a huge transfer fee.
"I would be really pleased if our fans would give him a better reception next time Bayern come to Signal Iduna Park.
"We should not forget that we are dealing with young guys here and Mario really is a nice guy. Those who know Mario can all confirm that he doesn't always come across like the guy he really is.
"The BVB hierarchy still have a great relationship with him. He visited us after the Supercup and we gave him a good hug."
Gotze made 116 official appearances for Dortmund between 2009 and 2013 before joining Bayern.