Sorry to hear that, don't be so hard on yourself in the future. This is hard work (even if it is fun). As a post-mortem you did one thing right and one thing wrong.

What you did right: You accepted responsibility. Good, this is a hard trait to find. The "perfect" engineer mixes equal parts intellegence and humility.

What you did wrong: You didn't trust your team. They were all very supportive of you, but you didn't trust their assesment of you.

Trust your team; trust yourself. Have confidence in your ability to learn from your mistakes.

You'll do fine. Start looking for another start-up job while working at a corp.

The best time to find a new job, is when you already have one.