It's fucking job terminations. You're GOING to be criticized no matter how you do them. The best approach is to just be robotic about it, and maybe throw in a platitude that amounts to, "It's not you, it's me".
"We need to layoff half of the company. I'm sorry and take responsibility. I have failed our employees and shareholders. Because of this, I am stepping down". That's taking responsibility.
"We had a major F-up. It was my responsibility. And here are the concrete steps I am taking to ensure it never happens again, along with the mechanisms you all have to hold me accountable. If these fail, the following bad thing will happen to me." That's taking responsibility
Also if one of your options for "taking responsibility" is quitting, I guess your view of the world is that you would also fire any of your employees when they mess up, when whole industries have recognized the need for blameless cultures where making mistakes is part of the learning process.
The phrase "I take responsibility" is never accompanied with any sign that the person does in fact take responsibility. It means more than just "Ooops, I did a bad"
Relevant discussion: https://news.ycombinator.com/item?id=33450753