"I think as a player, when you've come so close and you've been in the title race, then you know you're capable of going all the way and winning it," Evans told Liverpoolfc.tv.
"You gain confidence from that - not only in yourself, but also in the players around you.
"That's something you can never buy. No matter how great a footballer is, you have to learn to be a winner.
"We've done it in cup ties and competitions in recent years, but when it comes to the league it's over a longer period of 38 games and you've got to be consistent - that's exactly what we were last season.
"Having played so well and amassed so many points, Liverpool will be disappointed they didn't win the title, but they should take confidence from that, rather than any negatives.
"We could not have come any closer last campaign and I am very optimistic for next season."