Byrne has rejoined former club Scunthorpe United, but while Johnson admits that he would have liked to have kept the 31-year-old, he believes that the Irishman will benefit from the temporary move.
The 32-year-old told the club's official website: "You don't want to lose Cliff with the way he is, he's a great professional and was very good for me last year.
"But, as a manager, I've got to respect that he's so professional and so keen to be playing and, if I can't see him being a mainstay in my team for the immediate future, it's better for him to go and get some games somewhere.
"We had an offer just before the deadline, which I turned down for Cliff because I didn't think it was right for any party but being Scunthorpe, he's a legend there, they love him, he's going to play all the games. It was just right for Cliff really."
Byrne previously made 332 appearances during 10 seasons at Glanford Park.