The Northern Ireland international spent last week training with the Premier League side but it was revealed on Tuesday they would not be taking their interest any further.
Adams believes the ramifications of Everton's decision will be positive as the young striker now looks to help Vale secure promotion from League Two.
"Everton have been in touch with me, through James's agent, to tell me they won't be pursuing their interest," said Adams in The Sentinel. "They have enjoyed working with him and I would hope he will come back with more confidence.
"They are not saying it's a 'no' in the future. But at this precise moment in time he is not the type of player they are looking for.
"James has been up there and worked with good players, possibly better players than he's working with here. He now knows the standards he has to adhere to if he wants to be a top player."