Ben Youngs marked his 100th Test with a double as the visitors secured a 34-5 bonus-point victory over Italy in Rome to give themselves a great chance of winning the title.
Ireland would have been guaranteed the trophy had it beaten France by a margin of at least seven points in the final match of the tournament, but Les Bleus gave another demonstration of their huge potential in a 35-27 victory in Paris.
England finished level on points with France, but Eddie Jones' side won the competition for the first time in three years on points-scored difference.
Farrell says there is more to come from England after it was able to celebrate almost a year to the day since it was beaten by South Africa in the Rugby World Cup final.
Asked if England has more to give, captain Farrell said: "Massively, it feels like we're just getting started. There were four new caps today, someone who got their 100th cap in Ben Youngs and Jamie George who got his 50th.
"It feels like we've got a brilliant blend of experience and youth to drive us forward and being involved in training in the last few weeks has shown that to us and we're looking forward to what's in front of us as well."
Farrell paid tribute to wily head coach Jones after he masterminded the third Six Nations triumph of his reign.
He said of the Australian: "He's been brilliant. the best thing I can say is we all love being here and being in camp and we all love working hard to improve and hopefully you see that when we get out on the field."
The England skipper also hailed Youngs on a special day for the scrum half.
"I'm chuffed for him. It's a huge achievement reaching 100 caps, only the second person to do it for England, it's massive," Farrell said.
"To have such a good game, like he did, and to top it off with the trophy is brilliant."