Kris Boyd was the player hooked in favour of Cousin, who started the game on the bench because both he and fellow new recruit Steven Whittaker are still lacking match fitness.
Despite not being 100% fit, the former Lens striker quickly succeeded where Boyd has so far failed this season by finding the back of the net.
The Rangers boss said: "Both Daniel and Steven Whittaker are still well short of match practice but it's always easier for forwards in that situation to go on and show what they can do and thankfully he got us a goal.
"We are pleased with the effort that everybody is putting in. Kris Boyd has scored a terrific number of goals for us over the last couple of seasons.
"He's going through one of those spells that strikers go through when the goals don't come - but the goals will come for him.
"There will be plenty of opportunity for that to happen in the coming weeks."