The victory was in Robertson's 300th game for the club.
He said, "I knew the milestone was coming up. It's nice to tick these things off. 300 appearances is incredible. I'm delighted to play that many games for this great club. It's always nice to top these milestones off with a great result and I think you can class that as a great result.
"When I first signed I believed in myself. I wanted to prove myself at the top. I've loved every minute of it. To knock 300 games off with not many injuries apart from last season, is great. This season we've started really well and hopefully we can continue that.
"We look a bit more secure defensively. We had a lot more control in our game today. It was 3-0 and it could have been more. You can't argue with three great goals scored. A clean sheet is masssive. To come away to your big rivals like Manchester United and keep a clean sheet is massive.
"They always say clean sheets will win you things and that's always been the case when Manchester City have won the league and when we did. Three games without a goal conceded is really good and we want to keep that going.
"Alisson had too many shots to save last season. I think he's been happy with the people in front of him so far. It's about the whole unit working hard. The wingers put in an unbelievable shift and it helps the boys at the back."