Barrow beat the Knights 34-12 and have now won their last three Co-operative Championship fixtures.
Wright said: “The defence pleased me most. York had enough decent possession to cause us problems, but we scrambled and we worked well for each other.”
Coach Warren Jowitt said: “Luke’s injury is a big blow for us. He’s been my first choice hooker, and he’s been playing really well.
“It looked like he was getting back to some very good form against Widnes, so it’s a shame for him.”
Last week the Rams drew 34-34 with Widnes, and Jowitt now believes his side can recapture their good form.
He said: “It was a good result. We were really pleased because we’ve been in a bit of a lull.
“We’d lost four league games on the bounce, so to pull it round like we did… it put us back on the bike and it put some confidence in the lads.”