Which bible are you reading? Here's one passage of scripture to the contrary.:
...because if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For with the heart one believes and thus has righteousness and with the mouth one confesses and thus has salvation. For the scripture says, “Everyone who believes in him will not be put to shame.” For there is no distinction between the Jew and the Greek, for the same Lord is Lord of all, who richly blesses all who call on him. For everyone who calls on the name of the Lord will be saved. Romans 10:9-13
There are three notable action verbs in this passage: Confess, believe, and call.
When we confess with our mouths that Jesus is Lord over our lives AND believe in our hearts that God raised Him from the dead AND call on His name, we are bearing evidence to His free gift of grace. When we do (yes, do) all those things, we have accepted His grace.
It's the same as with a child at a birthday party. They see the gift lying on the table, ready for them to open it. But to accept it, they must physically walk to the table, summon the strength to lift the box, and open it. At that point, they have accepted the gift. If they leave it on the table, they have not accepted the gift.