Deep regrets also often go hand-in-hand with the good old "if," where you totally would be sorry if you had, hypothetically, done something bad (but you didn't). The mayor of Sunland Park, New Mexico, apologized by saying, "If I ever let [the citizens of Sunland Park] down in any way, I deeply regret it." Which is, to be fair, a big if, because all he's really admitted to was being so drunk while signing city contracts that he didn't know what they were, which he apparently thought would be a clever excuse to avoid paying the company he signed the contract with.
"If I tell them I was passing-out drunk, they'll have to let me keep all this! It's foolproof!"
So the guy either has a serious alcohol problem that interferes with his work, or he's retarded, or, more likely, both. Does this constitute "letting the voters down"? Who knows? Let's throw an "if" in there to be safe. And if he has completely deflated some voters' faith in their civic government? Is he sorry for what he's done? Ouch, that's a little strong. Best to go with "deeply regret."
People who deeply regret things often are pretty hazy on the specifics of what they did. When the U.S. General Services Administration got called on the carpet for spending over $800,000 on a Vegas trip, agency head Martha Johnson personally apologized to "the American people" for "the entire situation," which could technically refer to anything from the recession to global warming.