Since the event is in present perfect (you have invited your friend to a concert) and the present perfect always uses have/has + a past participle, you will still use have here, but in gerund, plus a past participle.

Something like this:

I’m sorry for having invited you to the concert

I want to apologize for having invited you to the concert

Here are more examples:

I’m sorry for having arrived late to the show. She apologized for having chosen that movie. It was awful!

We can use the structure there’s no need to + bare infinitive to give advice

“There’s no need to apologize” or to recommend something in the affirmative “There’s a need to improve the quality of the performance”