Goals in both halves from Barrie McKay and Martyn Waghorn sealed a comfortable win for the Gers, who kicked off their 2016-17 campaign with another 2-0 victory at Motherwell on Saturday afternoon.
Centre-back Hill and right-back Hodson were left out at Fir Park but enjoyed comfortable eveings at Ibrox last night, and the Rangers boss was pleased with his summer signings.
“It’s good to get the new boys in too”, Warburton told Rangers TV. "Clint Hill was solid and Lee Hodson came in and did very, very well and all over the park there were some very pleasing performances."
Rangers have signed nine new players this summer in total, with Joe Doodo arriving from Leicester City on Tuesday to become the ninth.
Jordan Rossiter, Joey Barton, Niko Kranjcar, Matt Crooks, Josh Windass and Matt Gilks make up the other six new faces at Ibrox.
Rangers, who have won both League Cup outings so far, visit East Stirlingshire on Friday night, before hosting Stranraer at Ibrox on Monday to conclude a gruelling period of games - four in the space of nine days.