The Red Devils' play-off hopes ended with a 2-1 defeat at Oldham but Barker believes his players can be proud of what they achieved this year.
He said: "To reach our 44th game and still be fighting for something was a testament to everyone.
"We have been in with a shout all season but we let our standards drop today and it cost us the game.
"We have looked a decent away team this season and we need to have high demands of each other if we're going to have aspirations to improve.
"At our best I would have fancied us to come here and win. Defeat is a bit harsh because we deserved something from the game, but we didn't see it through to the end. It wasn't quite there, individually or as a team."
Matt Smith fired Oldham in front after 56 minutes, bundling through to the edge of the box and unleashing a low shot into the bottom corner of the net.
Crawley levelled 13 minutes from time when a short corner routine ended with Mark Connolly converting a simple header from point-blank range.
The Latics' winner arrived in stoppage time as Jean Yves Mvoto met Jose Baxter's deep free-kick and headed home from four yards out.