After that disappointing opening 45 minutes at Ewood Park, Barry Murphy felt his side created good chances in the second half and should have scored a second goal.
Overall, however, he accepted his side fell short.
“We can have no excuses,” he added.
“We knew how tough the challenge was going to be today. We gave the ball away in really dangerous areas.
“By our standards, we weren’t good enough in possession. We lacked aggressiveness. We stepped back today and didn’t push forward. That cost us.”
Cardiff got themselves back into the game soon after the restart when Robinson drilled into the bottom corner to open his account for the season.
Fellow Republic of Ireland international Jack Moylan went close to scoring two fine solo goals, but the Bluebirds lacked the clinical edge to find an equaliser.
“We had really good situations, and with the players we have, we would back ourselves to find the correct solutions,” said Barry-Murphy.
“We pushed right until the end, I’ve got no qualms about that, but I do not want to shy away or make excuses.
“We have to be really clear and honest with ourselves that we were not good enough today. We have to take it on the chin.”
Cardiff will get the chance to put things right when they host fellow Championship strugglers Watford on Tuesday, 13 October (19:45 BST).