Bluebirds boss Cox saw his team go down 2-1 to Dagenham & Redbridge.
He was not at all pleased with their first half performance but after the interval Barrow were much improved. That fact he was happy with.
He said: "It's not always the end of the world if you lose on the first day of the new season.
"Providing, that is, that you quickly figure out where you went wrong and set it straight right away.
"We weren't up to it in the first half. We saw a side that didn't look like they had been playing together for long, which of course is true to an extent.
"We looked like we had lost players in the close season and that we were still building. We lacked spark but we were better in the second half."
Cox says Barrow could have even pinched a point.
"We came close, on another day we could have left Dagenham with a draw but we didn't quite have enough," said the manager.
"It's going to take a bit of time but I saw enough from that second half to suggest to me that we'll be alright once we find out feet.
"I'm not despondent. This was always a very difficult first fixture but now we have to show the improvement we showed in the second half in our next few games."