He said that others would be saved through believing the message about Him spread by the Apostles.
Last I checked, Luke wasn't an Apostle.
Those writings of Luke did go back to the Apostles. Luke put together the sources in Jerusalem and wrote them in order. He says so himself, and apparently, the churches verified this and passed this book down.
Additionally, of course, Luke was a participant with the (truly) main Apostle to the gentiles, Paul.
So, again, it goes back to the Apostles.