No, it's not true; people in the Old Testament did believe in life after death -- although their understanding was not as full as ours, because God has revealed more about heaven to us.
I think, for example, of Job in the Old Testament. He passed through sufferings that most of us can barely imagine -- not just physically but emotionally. Almost overnight, he lost everything -- his family, his wealth, his health, even his friends. In the midst of it all, he felt he might be dying, but instead of shrinking back from death, he welcomed it. Why? Not only because he knew it would bring an end to his sufferings, but also because he knew that if he died he would go to be with God. He declared, "I myself will see him with my own eyes. ... How my heart yearns within me!" (Job 19:27).
Or think of King David, who wrote many of the psalms. When his infant son was taken from him by death, David affirmed his conviction that some day they would be reunited (see 2 Samuel 12:23). And his words in Psalm 23 have brought comfort and hope to countless generations of believers: "Even though I walk through the valley of the shadow of death, I will fear no evil. ... And I will dwell in the house of the Lord forever" (Psalm 23:4,6).
This was their confidence -- and it can be ours in even greater measure, because Jesus Christ died on the cross to take away our sins, and He conquered death and Hell forever by His resurrection from the dead. Is your faith and hope in Him?