The Leeds head coach has been discussing the West Ham full-back.
Indeed, Evans believes Byram was unsettled due to his lack of confidence in Leeds' ability, which eventually led to a move to the Hammers.
The Scot told the BBC about the now West Ham defender: "If I look at last summer, Sam Byram never really settled. Sam probably never thought in his head that this was a promotion team.
"Next season, maybe these fantastic youngsters will be thinking this is a team that can win promotion."
Evans has recently been criticised by Leeds fans for making big claims that usually go unsupported.
The Scot's continual promises of jam tomorrow will likely prompt more of the same. Evans is adamant United will do well next season but isn't mentioning too much about what exact progress he is making in the here and now.
As for Byram, meanwhile, he could still be an FA Cup winner with West Ham, although they face a tough quarter-final draw at Manchester United and he himself is cuptied. In the Premier League, they host Sunderland and former manager Sam Allardyce later today.