Offer a sincere apology

Bad first impressions happen for a variety of reasons; perhaps you were late for an important meeting with a new contact and came across as unprepared. Or perhaps you unintentionally said something offensive or told a joke that was taken personally. Whatever the cause, apologise as soon as possible. You can do this in person immediately or send a short email afterwards. Apologising is direct and will be better than ignoring the mistake. But don’t overdo it; you may unintentionally make a sensitive situation awkward. Once you’ve sincerely apologised, move on.
Don’t be too hard on yourself

As a result of your nerves perhaps you didn’t make as much eye contact as you could have. Or maybe you glanced at your phone expecting an important message to arrive. Whatever the case, don’t beat yourself up over it. While the perceived mistake might be magnified in your mind, it might have barely registered in the mind of the person or group you’re talking to. Take note of the situation and be mindful of it going forward; there’s no need to draw attention to your actions. If you’ve learned from them, move on and let it go.
Be genuine

By being yourself you’re more likely to come across as natural and less awkward and forced. It’s OK to be honest and admit that you’re trying to make a good impression or that you’re a little nervous, but once that’s said make sure the next time you meet, you act as yourself. This reassures your new contact that you were indeed being honest and are who you say you are. If you have a great sense of humour, let it shine through. If you’re talkative, take a step back and listen attentively.