Sure, you can say, “God, I’m sorry.” Catholics believe that you have to feel, in some way at least, sorry for your sins (or sorry that you don’t feel sorry) before you can go to a priest to confess your sins.
You see, having guilt for your sins and then confessing them are just two means to an end. You must first do those two things, and then the priest does the ultimately necessary act, which is absolving your sins, in which he says, “I absolve you of your sins in the name of the Father, and of the Son, and of the Holy Spirit.” That is the moment in which you are released from the damnation of your sins. There is a case in which you can feel guilt for your sins and not actually go to confession and still be forgiven (this is called perfect contrition), but to receive forgiveness this way, you must have had as a desire to actually go to confession, but you couldn’t for some reason.
In the confession process, the priest also gives penance. This might consist of saying some prayers, or doing charitable works, or thinking more next time you are tempted to sin. Technically you must do this penance before the next time you go to confession, but most people do this soon after their confession.