The defender arrived last month from Sporting Lisbon.
"I loved playing in the game and it was a great win," Ilori told the Liverpool Echo. "I hope I can carry on winning at Anfield. Every player wants to play whether it's in the first team or the reserves.
"I want to get as many minutes as I can. I didn't have a proper pre-season due to injuring my hand but it's good to be back fit now. I'm enjoying it here. Brendan Rodgers seems like a great guy and a great coach. I will do my best for the club."