Definitions of regret:

• noun:   sadness associated with some wrong done or some disappointment

  Example: "He wrote a note expressing his regret"

• verb:   be sorry

  Example: "I regret to say that you did not gain admission to Harvard"

• verb:   decline formally or politely

  Example: "I regret I can't come to the party"

• verb:   feel sad about the loss or absence of
• verb:   feel remorse for; feel sorry for; be contrite about