The 26-year-old had his contract terminated by mutual consent on Monday and immediately joined Cheltenham, who are two points above the Millers in the table.
The move came as something of a surprise, given Evans had said Taylor was one of the first names on his teamsheet just before Christmas, but the boss insists things have changed.
"Kari Arnason was in central defence and David Noble was injured when I said that, those two are now available in midfield," he said.
"With us signing Claude Davis and Craig Morgan getting close to fitness that allows Kari to move into midfield and means we can move Jason on. He is a great kid and I wish him every success.
"It doesn't matter to me where he has gone, we're not at a level of football where we can dictate where they go. If he'd have gone to the top of League One it wouldn't have bothered me, if he'd have gone to the Conference, it wouldn't have bothered me.
"Me and all the staff thought the same, when we looked at the options and everyone fit, Jason just wouldn't play. He is a young man that wants to play, he has a real desire and we couldn't give him games."