I would say that it is wise to remember that the comma is a way of representing a pause, that the speaker makes, whilst talking.
In this case, as Lawrence points out in his comment, the clauses are rather short, and so there is no real need for the speaker to pause, to take a breath, or emphasise the first clause. Therefore, in this case, and other cases with short clauses, the comma can be omitted.
However, it should be noted that, one could still use a comma (in reported speech), if desired, in order to provide emphasis, by pausing, in order to allow the meaning, or significance, of the first clause to sink in to the listener.
That is to say, if the speaker, who is an invitee, was trying to avoid offending the listener, who could be the inviter, by refusing the invitation, pausing after the "I'd like to go" gives the impression that the speaker has a desire to participate (even if they don't really want to), before stating why they can't.