There's no such thing as a perfect parent, says Tovah Klein.

"Being a parent is so humbling. It's throwing at us probably daily [reminders that] we are far from perfect," says Klein, a child psychologist, author and director of the Barnard College Center for Toddler Development.

Fortunately, making mistakes and owning up to them is one way that parents can actually help teach their kids how to become healthy, successful adults. "Perfection is impossible, but it's also important that we're not [perfect], because our children learn how to handle real life," Klein tells CNBC Make It.

Even so-called experts are no exception. In her latest book "Raising Resilience," which was published in September, Klein shares some examples of moments she let her emotions get the better of her when raising her own three now-grown children.

Like most parents, Klein raised her voice in heated moments on more than one occasion: "I could really yell at my kids," she says. She points to "rough times" in the evenings when her children were younger and could become rowdy between dinner and bedtime.

The rowdiness could sometimes devolve into loud arguments that left Klein "embarrassed if people would have come over to my house at 6 p.m.," she says. Yelling is common, even understandable, in the heat of an argument, she adds — but it's far from ideal, and parents should commit to repairing the situation once everyone has calmed down.

"I wish I had never been that parent who went over the top and really got into battles with my children. But I did," Klein says. "And, when I did, I had to very shamelessly own it."

How and why to apologize to your kids

In her book, Klein writes about how these difficult moments create a "disconnection" in the relationship that can have harmful effects if they go unaddressed. Raising your voice or lashing out, even in a heated moment like a toddler's tantrum, can be disruptive and potentially scary for the child. 

A child might mistake their parent's outburst as something more serious and long-lasting. That can lead to self-blaming and shame, which can cause negative long-term effects to their mental health. Children who are regularly yelled at are more likely to develop behavioral problems, low self-esteem and depression, according to a 2013 study published in The Journal of Child Development.

Parents should quickly apologize to repair the relationship and put their child's mind at ease, says Klein. She recommends being "honest and direct." That can be as simple as saying, "I'm sorry I yelled," or, "I apologize. I shouldn't have done that."

Apologizing models exactly the sort of positive, mature behaviors parents want their children to emulate, according to Klein. It "brings relief to your child and provides a model of how to deal with anger and disruptions in other relationships in their lives" going forward, she writes in her book.

Accepting the fact that you can never be perfect, and being open with your kids about your mistakes, will benefit both you as a parent and your kids as they grow into mature adults, says Klein.

"I'm most proud of the moments that I could catch myself and [remember], 'You've got to be the adult in this room,' even when it was really hard to be," she says.

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