Campaigning in Edinburgh a day after her election, she said she had a mandate to change the party.
She declined to say which of the four UK Labour leadership contenders she would vote for but said she would be "delighted" to work with any of them.
She urged former supporters to give her a chance by listening to her arguments.
"One of the first things I said when I was elected was that I'm not asking for people's vote straight away, I wouldn't be so presumptuous," she said.
"I'm just asking for their ears, for a chance to be heard."
Ms Dugdale was joined at The Meadows by shadow Scottish secretary Ian Murray, Labour's only MP in Scotland, and Alex Rowley, the newly-elected deputy leader.
Asked if she took any responsibility for Labour's loss of 40 Scottish MPs in May, the former deputy leader said: "I never shied away from taking my responsibility for what happened in the general election.
"Party members who voted in the contest that concluded yesterday knew that - but I got 72% of the vote," she said.
"That's a huge mandate to change the Labour party."
The Lothians MSP refused  to be drawn on which of the UK Labour leadership contenders she supported.
She said: "The message I can get across is to say that decisions about the Scottish Labour Party will be made here in Scotland and they will be made by me."
Ms Dugdale comfortably saw off a challenge from fellow MSP Ken Macintosh for the leadership. Labour MSP Alex Rowley, a former aide to Gordon Brown, was elected as the party's new deputy leader.
New Scottish Labour leader Kezia Dugdale has promised she will decide the future direction of the party in Scotland.