The 16-year-old became the seventh youngest player to play in England's top flight when admirably performing a midfield role in his side's shock 2-0 win over Arsenal at the Emirates Stadium.
Oxford was instrumental in keeping a dangerous Gunners midfield under control and his debut performance was certainly not lost on a very proud Bilic.
"He has a presence, he's mobile and quick, and he can turn and pass the ball, not just square balls," said Bilic who was in his first game as a Premier League boss.
"He's not fazed about playing at the Emirates. I tried to help, I told him whatever he did wrong was my fault not his, but I'm lucky he didn't do much wrong.
"He's definitely going to be a big player. Let's be fair, (Mesut) Ozil had his moments but it's not easy to minimalise the game of these world-class players.
"He didn't know until yesterday that he was going to play. We talked the night before but it wasn't like, 'let's sit in a dark room, I have to tell you something Reece, you're going to play'. It was more like chatting.
"That would make pressure. This was natural for him. For today, it was a good decision. He's definitely going to do it [succeed], there's no doubt."