Stephen Clemence felt Barrow should have ended a two-month run without a League Two win after a 1-1 draw at Bradford.
Robbie Gotts put the Bluebirds in front with only their fifth away goal of the season.
But the league’s top scorer Andy Cook took his personal tally to 10 with Bradford’s equaliser.
Barrow head coach Clemence said: “I thought we were the better team.
“We would have liked to have got the second goal to put the game to bed. But to come here, silence the crowd and handle the ball like they did gives us something to build on.
“I’m really pleased with the performance because we all know it’s a difficult place to come. We’ve worked hard on the training ground the last 10 days and I felt we did a lot better with the things that haven’t been going for us.
“They were always going to have pressure in the game and you can always pick faults in goals.
“There were faults in our defending for Andy Cook’s goal. But they haven’t had any other clear-cut chances apart from that.
“There’s obviously a bit of unrest but that’s nothing to do with us. That’s something you’ve got to try and do as the away team at these sort of places.
“It takes a lot of courage from the players and they showed that in abundance.”
Both teams have been struggling for goals and that was evident in a poor first half.
Andy Dallas fired over the bar early on for Barrow while keeper Paul Farman saved from Olly Sanderson and Alex Pattison.
Gotts put Barrow ahead in the 58th minute with a near-post finish set up by Ben Jackson.
Cook salvaged a point for the home side when he headed in Bobby Pointon’s cross in the 79th minute.
Bradford manager Graham Alexander said: “I don’t think anyone deserved to win the game. It was very stuttery.
“A lot of that came from us overthinking passes and runs and a lot from the amount of free-kicks that were given.
“Both our strikers got booked in the first five minutes, which I’ve not seen before.
“But we just didn’t play with a fluidity and a pace in our decision-making. It made it a stunted game.
“We conceded a goal we were disappointed about but it gave us a ‘nothing to lose’ attitude and then we found the speed in our play.
“Bobby had a lot to do with that with how he played and gave us that extra composure. Aden Baldwin did as well when he came on.
“It’s a point from being a goal behind but I think it’s two points we’d have liked more.
“If we’d have played better, we would have had the opportunities to do that.”
