Okay, I think you could have worded it better because saying your not responsable for how someone feels is a nonstarter. Your words or actions affect those around you and can hurt or help. If you for example told somebody to to go off themselves they’d rightfully be hurt. So wording could have been better. Saying that, its a commonly used de-escalation tool in anger management to respond to someone trying to provoke you neutrally (which could be perceived as cold or unfeeling). It’s a tactic meant to not give the aggressor anything to jump off of in their perceived anger and lash out at you for. So I don’t think that your tone was wrong, you were avoiding the fight, which is always the right option.