Scotland completed their Six Nations campaign with a 21-8 win over Italy at Murrayfield, earning a first victory of the tournament at the fifth and final attempt.
They next play warm-up fixtures with Ireland on August 6 and Italy on August 20 before their opening World Cup encounter with Romania in Invercargill on September 10.
Georgia, Argentina and England follow in the group stages, with two teams progressing to the quarter-finals.
Robinson said: “We’re going to go to New Zealand willing to play, as I think we’ve done in every game in this championship.
“We’ve gone out and really tried to play rugby by moving the ball and trying to attack from anywhere.
“I’ve been delighted about that. You saw that in France, you saw that at Twickenham.
“That’s the development the team has made in this championship.”
Scotland lost to France (34-21), Wales (24-6), Ireland (21-18) and England (22-16) before finally securing a win on Saturday.
Scotland had a record of five wins in six Tests entering the Six Nations and were expected to perform well.
However, Robinson has always warned Scotland must be firing on all cylinders to win any game and he reiterated that when referring to the World Cup.
“There’s a lot of hard work to be done,” he added. “The first two games I think are going to be crucial for us, playing Romania and Georgia, and we’ve got to focus on those two games.
“I think they’re potential banana skins for us, the way they play. They’re pretty physical, they’ve got a good scrum and lineouts – playing a side like Italy is very similar.
“We’ve got to get through those first two games and then enjoy the fact we’re playing Argentina, who we performed well against over in Argentina.
“We enjoy playing against them and we’ll see what happens.”
The Six Nations has seen Scotland adopt a more expansive approach.
At the heart of that has been fly-half Ruaridh Jackson, who has grown into the number 10 jersey since starting against Ireland in place of Dan Parks.
Jackson was influential in the build up to Scotland’s opening try on Saturday. With Scotland trailing 8-6 early in the second half, Jackson’s break led to the ball being recycled and Nathan Hines feeding Nick De Luca for the hosts’ first try at Murrayfield since November 2009.
Nikki Walker added a second soon after and Chris Paterson kicked 11 points.