The Sky Blues showed two sides to their game to overcome the League One leaders 1-0 at the Ricoh Arena.
They dominated Ronnie Moore's men in the opening period and should have had more to show for it than Leon Clarke's 19th-minute strike from close range. But Rovers came back at City in the second half and the hosts ended up hanging on.
Robins said of his team: "They showed winning qualities. I thought we played really well in the first half. We played less well in the second half.
"They changed their shape for the first time this season which was a compliment to us and we showed that they warranted doing that in the first half because I thought we passed it really well.
"We deserved the lead. All the stats were in our favour in the first half and in the second half I thought they edged it.
"We started to become a little bit sloppy and they caught us on the break and outnumbered us a couple of times and it took an inspired Joe Murphy to get us out of the mire and keep a clean sheet.
"The important thing was the three points and the players have come up trumps so I am delighted on two fronts."