Communication is the key.
Targets can change, but that should not come to anyone as a surprise. If your theoretical (on-paper) targets are not aligned properly with the actual work, then there's surely involve a gap which will make you look bad despite delivering the assigned work.
As gnasher729 already mentioned, you should have had this conversation earlier, but better late than never. You need to do it now.
There's no reason to assume that the CEO is unaware of the change in priorities, however, until you communicate that the additional tasks are going to delay the initially agreed upon targets, no one can know that. I'll advise it to break it down in two steps (in the following order):
Have a discussion with your manager.
Thank them for a nice work environment, then explain the situation, and mention that you need to clear things up about the expectations (which are not going to be met) and you need to have the targets re-calculated. Also mention, you need to have the CEO informed of this and request your manager to backup your statements.
Have a meeting with the CEO.
Unless you manager explicitly takes the onus on getting the targets re-aligned with the CEO, go ahead and have a meeting, present your case, and inform that you already had a discussion with your manager about this.
In general, always follow couple of best practices:
For every work assignment (which is not a "quick help" or a code-review sort of activity which can be done in couple of hours), make sure it is aligned with the overall target.
If there are priority items, or unplanned activities that you need to work on / take care of, make sure they goes on record, and have the target revised as needed.
Also, make sure your contribution and achievements for all the tasks / deliverable are noted down.
Having said all these, answering the exact questions:
Shall I explain to the CEO what went wrong and explain to him how I have been involved in other urgent projects by my manager because of which I did not get enough time? But then would it not damage my relationship with my manager? I cant afford that.
Yes, you need to let the CEO know. There's no reason to assume that the CEO is not aware of the additional tasks, but they are unlikely to be aware of the possible slip in your targets due to the additional work. As I proposed, if you have a meeting with your manager before directly reaching out to the CEO, it'll remove any chances of misunderstanding between you two.
Should I leave everything and now concentrate on my goals explaining the problem to my manager and requesting him to exclude me from those things which are not directly related to my goals?
Not really. If the manager was assigning you work without the knowledge and approval of the CEO (bad business for you), that needs to be corrected. If your manager kept the CEO updated, there's no problem. It'll clarify your doubts and confusions.
Shall I own the failure and ask the CEO to give me one more month and concentrate on my goals (requesting the manager not to bother me further)?
As of now, it's not your fault. Have the discussion as mentioned above.
What is the best that can be done here and how to avoid such a catch-22 situation in the future? Catch-22 because I can't blame my manager for the failure and at the same time must explain why I am failing.
Once again, it's not a failure, yet. There's change in plan, and you need to ensure all are aware and on-board with that change.
Best of luck!!