Regret

Regret may refer to the following:


 * High Prophet of Regret- The Covenant leader.
 * Regret (Level)- The level in Halo 2.

Speculation
The message intercepted by Cortana, an AI, durning the Earth Invasion was the repeating message "regret, regret, etc...", possibly referring to the the Covenant's discovery of Earth by accident, and not having enough forces to defeat it.