The England captain, starting his second stint as international skipper, guided his side to a 50-9 victory in their opening match at the Stadio Flaminio.
England ran in seven tries, including a hat-trick from Jason Robinson, while fly-half Paul Grayson scored 20 points as understudy to the injured Jonny Wilkinson.
But Dallaglio insisted there is more to come as England seek to keep the momentum gathered by their World Cup triumph in Australia.
"When you're the number one side there is always a high bounty on your head, but winning the World Cup has raised that bounty to a higher state," said Dallaglio, who took over as skipper from the retired Martin Johnson.
"The secret is how you handle that and take the side to the next level. Johnno did an incredible job as England captain and it is important for me to be confident and have my own identity.
"We wanted to set a new standard post-World Cup and we are perfectly pleased with the performance. We can build on this."
One man delighted with his afternoon's work was Robinson, who started his first international at outside centre and bewildered the Italian defence with his mazy running.
"We have got such strength in depth. I think we have shown that we are still the team to beat," said Robinson.
"Personally the big buzz for me is running the ball back at the opposition and my first try was good for that."
But if it was a game to remember for Robinson, what must it have been like for his 23-year-old Sale club-mate Chris Jones?
Jones came on to make his debut as a replacement for Joe Worsley in the final 10 minutes and promptly surged three yards from the base of a ruck to score his first try for his country.
It set his mobile phone buzzing with "at least 60 texts" and gave him a memory he will treasure for the rest of his life.
"To get on and then get my first try, I'm pretty happy," said Jones. "The ball just popped out. I grabbed it and went for it. It is not the furthest I've ever gone for a try, but they all count."
