England had to rely on six penalties from fly-half Toby Flood to seal the 18-11 victory but finished the match with their backs to the wall and had Italy No.10 Luciano Orquera been more accurate from the tee, Robshaw and co may have suffered a first ever defeat to the Azzurri.
But a fourth victory in a row maintains England's pursuit of a first Grand Slam since 2003 with a mouth-watering showdown with Wales in Cardiff scheduled for Saturday.
England head to the Millennium Stadium in pole position but a Wales win by eight points or more would see them defend their RBS 6 Nations title while should Rob Howley's men triumph by seven points they would still clinch the trophy, provided their try count remains higher than their visitors'.
But Robshaw admits he's just happy to see England maintain their winning record over Italy, claiming improvements must be made before travelling to Wales.
"Of course it was closer than we would have liked, it was important to get the win and we were under no illusions how hard it was going to be," he said.
"We were poor, but it's a win at the end of the day.
"There were moments where I thought we played very well but it was that final bit of execution that let us down. I thought our defence was a bit better, but there's a lot of work to do ahead of going to Wales next week.
"We work hard on our defence and it's a mindset, at the end of the day. We know they scored and came close a couple of times, but credit to all of the guys.
"We'll rest up, it's about being professional and this week is very much a mental exercise, and we need to make sure that mentally we have the right game plan and make sure we go there and do what we've got to do."