Yes he did. Neither did james and lily deserve to die, but he didn't care. Sirius didnt deserve to be in azkaban but he still did nothing. Harry didn't deserve to live in an abusive household, but he still sent him there.
^ if Harry hadn't lived with Dursleys, he would be long dead...he had no proof Sirius was innocent and surely he cannot break into Azkaban for saving Sirius...I know James and Lily didn't deserved to die...It wasn't from any angle Dumbledore's fault....
Dumbledore was known as the most powerful wizard and harry us supposed to be save when he's with him. He could ask them to give sirius veritaserum. He took their invisibility cloak when it could have helped them alone.
^ Invisibility cloak WOULDN'T HAVE MADE A BLOODY CHANGE!!! Do you think that you can escape the Dark Lord with a mere invisible cloak....No...and do you think Ministry will give a trial to a committed criminal... Sirius didn't receive a trial and thats not Dumbledore's fault and nobody blames him for this...Even Lupin thought Sirius was innocent but did he do anything...I am not blaming Lupin or any other Order Member for this then why blame Dumbledore....