The ex-England boss was reappointed by the Rams on Wednesday and takes charge for Saturday's home game against Leeds.
But he is mindful of his acrimonious exit in 2015 after constant speculation linking him with Newcastle United.
"My mistake was not quashing that, not dampening that and not committing," McClaren, 55, told BBC Radio Derby.
"That's my fault and I apologise for that. By the time I committed to the club, the club had every right to sack me.
"From my point view there was sadness, regret and disappointment how it ended the last time."
McClaren joined the Magpies in June 2015, a month after he left Derby, but won just six of 28 Premier League games in charge before being sacked for the second time in 10 months in March 2016.
He said he felt "lucky and honoured" to come back and work with "some damn good players" at Derby.
"The potential is there and to have a group like that, I am very lucky," he added.
"Now we have to work together and produce a team that supporters can be proud of - and that is what we want to do."
You can hear the full BBC Radio Derby interview with Steve McClaren by following this link.
Returning head coach Steve McClaren has apologised for the lack of commitment that led to his sacking by Derby County 17 months ago.