Eddie Jones's side ended a 12-Test winless streak against the Springboks courtesy of a 37-21 victory at Twickenham in their opening autumn international yesterday.
The result extended England's winning run to 11 matches, but Robshaw insists that there is no danger of the team becoming complacent.
"It's massive because I've played a number of times against South Africa and it's been a fixture in which you feel you're quite close, but you're not actually," Robshaw told reporters.
"For us to get over that and get a comfortable scoreline is a great feeling. To see our hard pay off is great for the squad. We left some points out there and we're a little bit disappointed to have conceded that last try, but as this series continues we'll get more fluid and show a bit of consistency.
"We always want to improve on last season and when we first met up in the summer, we were very clear that yes it had been very good and we achieved what we wanted to, but it's been about kicking on. You're only judged on your next result, so it's been about making sure that every time you go out there you produce as well as you can and keep things ticking over."
England's next match will see them take on Fiji next weekend.