The noun regret has 1 sense (first 1 from tagged texts)
1. (5) sorrow, regret, rue, ruefulness -- (sadness associated with some wrong done or some disappointment; "he drank to drown his sorrows"; "he wrote a note expressing his regret"; "to his rue, the error cost him the game")
Overview of verb regret
The verb regret has 4 senses (first 4 from tagged texts)
1. (8) repent, regret, rue -- (feel remorse for; feel sorry for; be contrite about)
2. (2) regret -- (feel sad about the loss or absence of)
3. (1) regret -- (decline formally or politely; "I regret I can't come to the party")
4. (1) regret -- (be sorry; "I regret to say that you did not gain admission to Harvard")