Kyle Lafferty made it four goals in three games for Hearts to cancel out Jason Brown’s powerful header but Rory McAllister scored a late winner, leaving Cathro open to criticism.
He said: “I’m not going to stop it, so let it be.
“We’re disappointed and our expectations are to do better. We didn’t start particularly well, and it allowed Peterhead to be motivated to keep fighting and keep pushing.
“We probably got ourselves on top, but we need to make better decisions to make sure we can create the opportunities and be more efficient in taking them.
“We were looking to put ourselves to the top of the group and haven’t done that so we’re disappointed. But we also respect that we have a number of new players in the team and there are relationships building.
“We need to make sure we’re ready for Saturday first and foremost. The demands we put on ourselves mean we want to beat Dunfermline, but we now need to do so to progress in the competition. That’s the reality.”
Peterhead boss Jim McInally said: “I was going to take Rory McAllister off but I remembered that if we made it to the final whistle we’d have had penalties - he’s our number one penalty taker!
“I wanted the players to go out and show they can play, but to win is a massive bonus. We’ve now got a chance of going through if we beat Elgin on Saturday.
“Everybody had written us off and you get annoyed because you don’t get respected at this level.
“I read the press today and nobody even mentioned Peterhead, so I told the players to go away from here with people talking about them and they’ve done just that.”