Regretfully acknowledging means expressing disappointment or sadness about a fact or situation. However, there are several synonyms to convey the same sentiment. "Admitting with regret" emphasizes that you feel bad about it, while "conceding with sorrow" implies a similar emotional attachment. "Accepting with remorse" is another option that connotes a sense of guilt or remorse. Similarly, "acknowledging with sadness," and "recognizing with disappointment" can express the same feeling of regret towards a particular matter. Overall, there are several ways to phrase a statement to acknowledge regret for something, and using different synonyms can help convey nuanced meaning in your writing.