Maybe you are not looking for advice but it might help...
First, dont say sorry for things that you have no power to change or choices that you have to make to meet the priorities and needs of your patients. Just dont. You wont get forgiveness. Patients are unwell, in pain and afraid and very few care how you feel about anything when they are distressed. Some will never care even when you relieve their distress.
Second, agree with them. Legitimise the distress and help them to articulate why they feel the way they do. This is how they may see that you understand what they are experiencing. They may even be open to you being honest and explaining why. Examples include 'It is frustrating to be left waiting isn't it? I have been attending to a deteriorating patient/got stuck in the lift/delivering a baby' or 'How long since you have had any food or drink? You must be feeling hungry/thirsty. Maybe we can do something to help until you can safety eat (NGT?)'.
Thirdly, dont rely on colleagues to dissipate patient aggression/anger. They may be feeling the same as you and one day other staff may be relying upon you to dissipate patient aggression. Sit down and ask your colleagues how they deal with it. What do they do? What emotional work do they do to look past the attitude, to see the patient?
Lastly, sometimes the best thing to say is nothing. Listen, let them rant. Overtime you will learn to disconnect your identity as a caring health professional from your authentic personal identity. You will recognise that you no longer say to yourself 'I dont deserve this'. Recognise that sometimes nothing you do or say will make any difference.
*Based upon 2+ decades of dealing with patients in distress.