The supporter ran towards Walker and the two exchanged words.
Walker then pushed the man in the chest before he was escorted off the pitch by City stewards.
"I hope no action is taken against Ian," Adams told Sky Sports TV.
"First of all the fan shouldn't have been on the pitch. I know he was unhappy but there were 30,000 out there just as unhappy and they stayed in their seats.
"I was worried about the safety of my player because anything could have happened to Ian and certainly he felt threatened by the supporter."