By Anne Fisher
July 31, 2013

FORTUNE — Dear Annie: Your recent article mentioning the Peter Principle — which dictates that people tend to get promoted beyond their level of competence — caught my eye because I’m a little worried that it might apply to me. I’m 29 and just got moved up to a job where I’m now managing my team of account executives at an ad agency, even though they are all older and more experienced. (In fact, two of these colleagues trained me when I was hired three years ago.)

This is really awkward. I’ve never been a boss before and, to tell you the truth, I’m surprised I got this job. I’m sensing a lot of resentment from several of the people who were my teammates, to the point where they seem to be dragging their feet (missing deadlines, etc.), which means I have to talk to them about their not-so-great performance lately, and I am totally dreading that. Any suggestions? — Ethelred the Unready

Dear E.U.: Interesting historical reference, there. Here’s another one: “Machiavelli wrote, ‘It’s better to be feared than loved, if you cannot be both,’” notes Brad Karsh, head of Chicago-based JB Training Solutions. “People tend to forget the second part. Managers should aim to be both respected and liked — but if you have to pick one, respect is better.”

Karsh is co-author of a new book you might want to take a look at, called Manager 3.0: A Millennial’s Guide to Rewriting the Rules of Management. It’s full of mini-case studies from Zappos, Groupon (GRPN), Southwest Airlines (luv), Google (Goog), and other companies with lots of young bosses.

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Given current U.S. demographics, that may soon describe most companies: Although Millennials (born between 1981 and 2000) often look to older workers like they are “just kids,” the Bureau of Labor Statistics projects that Gen Y will outnumber Boomers in the workplace by 2015. Since the number of Gen Xers is too small to fill all the corner offices vacated by retiring Boomers — who are turning 65 at a rate of 10,000 a day — many Millennials like you are stepping into management jobs.

“It’s a tricky situation,” Karsh notes. “But bear in mind that your uneasiness is only partly age-related. Almost every brand new boss, at any age, has doubts and jitters. It’s a tough transition because you’re moving beyond your comfort zone and onto unfamiliar ground.”

Moreover, regarding that resentment you’re sensing, Karsh wonders whether you might not be imagining at least some of it. He has done leadership coaching at companies where “new, young managers are seeing more resentment than there really is. They see it because they expect it.” Maybe there’s some reason why your team has been blowing deadlines that has nothing to do with you. It can’t hurt to ask.

Meanwhile, Karsh has three suggestions for building your credibility and “proving to your team, and yourself, that you deserve this job.” First, he says, “you have to acknowledge that, yes, your former teammates do have more experience than you do — but that isn’t all it takes to be a boss. Things will get better, slowly, if everyone sees that you’re working hard and making good decisions.” Get used to the idea that winning the team’s respect could take six months or even a year, Karsh adds: “There is no quick fix. It takes patience.”

At the same time, Karsh suggests, “Tap into all that experience your colleagues have. Ask for their input on decisions. Even if you decide to go a different way, acknowledge that you’ve considered their point of view.”

Millennials as a group tend to be skilled at collaborating, he says, so use that to your advantage: “You don’t want to be too collaborative” — it has to be clear that you are The Decider, as George W. Bush famously said — “but taking into account more experienced people’s perspective can make you a much better manager.” Not incidentally, it may also help mollify your detractors.

Third, Karsh says, even with people you already know (or think you know) well, put some extra effort into relationship-building. “Sit down with each of your direct reports one by one, and talk about their jobs — not the details of specific projects, but how they see their future, what they like and don’t like about what they do, and how you could make their work go more smoothly or be more rewarding,” Karsh says. “Everyone is motivated by different things, some of which you may never have thought of. You might be surprised by what you hear.

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“Whenever possible, talk with people in person, not via text or email. Millennials have been raised with technology, so they tend to rely on it, but face-to-face conversations work much better in your situation,” he adds. “It also doesn’t hurt to say, ‘Hey, let’s grab lunch’ once in a while. The more you work on creating trust and communication, the more readily your team will accept you as their leader.”

It might help to keep reminding yourself that the higher-ups who promoted you evidently believe you can do this job, or they’d have picked someone else. Even so, “don’t hesitate to bring up ideas and issues with a mentor, or ask human resources for some formal training,” Karsh suggests. Either or both are, he says, “really helpful for turning raw talent into management skills.” Good luck.

Talkback: Are generational differences an issue where you work? If you report to a much younger boss, how’s that going? Leave a comment below.

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