Within 20 minutes, Cardiff led 13-10, but whilst Scotland international Grove questioned some refereeing decisions, the 22-year-old said Edinburgh had to cut out the mistakes against Northampton Saints this weekend.
"Having watched the game as a team, we have realised it was individual errors at times that let us down - unforced errors," said Grove, currently on loan from Worcester Warriors.
"There were poor moments in attack when we should have been more clinical and come away with points and we didn't.
"People might say certain decisions from the referee made the difference in the game and Chris Paterson shouldn't have been yellow carded, and maybe they're right.
"But our lack of accuracy at times with ball in hand cost us and we've got to improve on that as individuals and as a team and move forward and get the wins we deserve.
"We went there out win - we didn't go to get a losing bonus point."