Both "OK" and "Thank you" are good answers to conclude that part of the conversation. Their response of "Don't worry about it" can also be a conclusion to the conversation.
Which one to choose depends on how sorry you feel about failing the request and how likely it was that you would have gotten the tickets.
If it was really unlikely from the start and they just asked you in case of that very slim chance of stil getting the tickets it's perfectly fine to not respond at all. Just continue with regular smalltalk like you usually would.
You've got your own responsibilities (work/kids/hobbies/...) and really didn't have the time to get them earlier. Your friend realises this as well so there's no reason to feel guilty about it. They really mean it when they said "don't worry about it". No harm was done here. Just a simple "OK" to aknowledge their response and then continue about other things.
over the top guilt
In case you had all the time in the world and it's entirely your fault that you didn't get the tickets. You may have explicity explained how it's your fault and that you're sorry about it. They respond with "don't worry about it" meaning they value your friendship over you not getting their tickets. In this context it makes sense to say "thank you" to show how relieved you are that they don't want to hold this against you.
From how you wrote the question I'd say you're somewhere in between the last 2 cases. OK would've probably been fine. Thank you might be a little too much but that doesn't make it a bad response. At this point it depends more on your body language and how you continue after this sentence.
I myself would've probably gone with a slightly more casual form of "thanks" with a smile and redirect the conversation to something different.
Since they did have an alternative, albeit a bit inconvenient, there's no real harm done anyway. Them asking you for a favor (that you sadly couldn't fulfil) is something different than you making a hard promise to get those tickets.
TL;DR: OK/Thanks/thank you/... are all perfectly viable answers as long as it's done with a possitive body language to support it.