Jonny Sexton was the key performer with a 16-point haul including one of four tries for the visitors - the others a penalty try and one each for Gordon D'Arcy and Ian Madigan.
Prop Willem Nel scored an impressive late consolation for the hosts but Bradley was left to rue the chances they failed to convert.
"We competed in patches against a very good Leinster side, that is a quality outfit, but it wasn't enough," he said.
"The crowd were fantastic. That, combined with the Willem Nel try are the immediate positives we can takes from this match but we have to take the chances that we create - Leinster were much better at doing that than us."
Bradley also felt a spell of six minutes before the break proved crucial in the overall outcome. With the score level on 34 minutes, a penalty try was awarded to Leinster with Edinburgh's Dave Denton sent to the sin bin.
And the Irish Province immediately made their man advantage count through D'Arcy's try before the interval, leaving Edinburgh two scores behind.
"The critical period was the combination of the yellow card, the penalty try and the score conceded when we were a man down," said Bradley. "But ultimately they had too much power for us."