The components of a strong apology include the recognition that you were in the wrong, the ability to make amends for your behavior by righting any wrongs and making a commitment to prevent your behavior from recurring in the future. While acknowledging that you are sorry is a crucial component to a strong and meaningful apology, you can apologize to someone without verbally saying "I'm sorry," though your apology may not be taken as seriously.
Offer a Solution
Actions that warrant an apology usually indicate you did something wrong, inconsiderate or hurtful. Offering a solution to the situation that you are apologizing for can show that you are willing to make adjustments to your behavior and work toward preventing similar situations form arising again in the future. Saying "It's unfortunate that your goldfish died because I overfed it while you were away, but I'll be happy to buy you a new one" is a solution-focused way to apologize, although it lacks empathy toward the situation.
Acknowledge the Other Person's Feelings
Situations that require an apology usually result in someone feeling hurt, used, offended or angry. You can apologize for your actions by acknowledging your compatriot's feelings during your apology. Making a statement such as "I understand that I hurt you and I promise not to betray your trust in the future" both acknowledges the feelings that you caused while also offering a solution to your future behavior. Because this apology lacks the acknowledgment that your actions were at least partially to blame for the conflict, it may come across as insincere or indignant.
Asking For Forgiveness
Asking for forgiveness acknowledges that you did something wrong and that you are aware that what you did resulted in hurt or betrayed feelings, but may not outright state that you feel remorse for what was done. While a statement such "please forgive me" clearly asks forgiveness, saying something like, "What I did was completely uncalled for, please forgive me" shows remorse for your actions without you having to say the words "I'm sorry."
Why Saying I'm Sorry is Important
Saying I'm sorry when offering an apology both acknowledges that you did something that was seen as hurtful or inconsiderate. Taking ownership over both your actions and the consequences of your actions is often the first step in asking for forgiveness and working toward rebuilding the bonds of your friendship or relationship.
Repercussions for not Saying I'm Sorry
While you can offer an apology without stating that you are sorry, you run the risk of your apology coming across as insincere, pious or unapologetic. Offering a poor apology may prolong your conflict, leave you in an undesirable social standing or may put your relationship or friendship in a position where it may not recover, even after a proper apology is offered.