Hi!
I'll split my answer in two...
1) “I’m sorry you’re leaving us” = "Siento que nos dejes" = “Lo siento/lo lamento” (Where “lo” refers to “que nos dejes”)
In Spanish, “que nos dejes” is subjunctive, so it is expressing subjectivity (thinking or feeling). One of the meanings of sentir is “Tener por triste o doloroso algún acontecimiento”. This meaning is very similar to expressions used to offer condolences, like “Lo siento (mucho)” = “Siento mucho la muerte de tu padre”. But as you can see, in this expression the subjunctive is not used.
2) "I feel that you're leaving us" = …
According to Michael Swan’s Practical English Usage, “feel” has different several meanings, but the one that applies here is that “feel” is often used to talk about reactions and opinions. The English sentence “I feel that you’re leaving us” should be interpreted as “I believe/think that…” and not as something you can touch. (If you’re a English native Speaker, you can clarify of this is true or not.). I’m not saying that it means that we don’t use our senses, because after all, in order to have an opinion of something we have to experienced our reality.
In Spanish “sentir” has also this meaning of “juzgar, opinar…” and even that of “presentir” or “have a feeling that”. So…
"I feel that you're leaving us" = “Siento que nos dejarás”.
As you can see, an indicative future tense “nos dejarás” is used instead of a subjunctive. While expressing an opinion, this sentence also affirms something as an objective fact. However in an university level “siento” is not usually used to express an opinion, and I also believe that in order to avoid confusion is better to say
“Me parece que nos dejarás” / “Creo que nos dejarás”
In short, if there is an Spanish subjunctive, be it present, past or future tense, its a regret. But if not, it's probably an opinion. In the sentence you provide in Spanish, it is definitely a regret.