At times the world champions looked clumsy and struggled to retain possession despite comfortably seeing off Les Bleus in a 3-0 whitewash, and Hansen could not shake the feeling that a far more comprehensive performance could have been achieved instead of the 24-9 win on the night.
"I wouldn't say we're completely satisfied," he said.
"The poorest part of our game was our ball maintenance, and, going into the next series, we're going to have to improve that."
The All Blacks will need to take another step up when they defend the Rugby Championship in August.
In perfect conditions at Yarrow Stadium it was apparent they had not yet mastered the new game-plan Hansen introduced in the first two Tests.
In his first international appearance this season, star fly-half Dan Carter did not look comfortable under the structures that Aaron Cruden had had a chance to adapt to during his absence in Auckland and Christchurch.
However, Cruden's performance during a clinical 30-0 win last weekend is proof that, when executed right, Hansen's kick-run blueprint has merit.
All of Carter's 95 Test caps were called upon in the clutch and he slotted a vital penalty goal to earn his side the lead for the second time, amassing a total of 14 points with the boot.
"(The game) wasn't easy for DC (Carter)," Hansen said.
"I think he would like to have another Test match next week to have another go.
"As we saw with Crudz (Cruden) it takes a bit of time to get into the saddle."
Conversely, France fared better with Castres pivot Remi Tales conducting what Hansen labelled a "smart" game-plan.
His creativity and willingness to take on the defence should give him an edge over Camille Lopez and Frederic Michalak, who each started a Test on tour.
Adding spark on attack, Tales almost set up a try in the opening five minutes which would have added to Florian Fritz's dropped goal for a 10-0 lead.
It was clear from the start that France were going to throw everything at New Zealand in a bid to avoid a whitewash.
"France definitely turned up to play; they probably played their best match," Hansen said.
Securing his first series victory as captain, Kieran Read led the All Blacks admirably but was not immune to his own share of basic errors that overshadowed the performances of many, including Victor Vito.
The Hurricanes blindside's reputation took a blow when he began his night with a knock-on and then failed to produce the physicality Hansen wants from his number six.
Read rued a lack of intensity at the breakdown in the first half but lauded the effort to turn things around after the break. Local hero Beauden Barrett made the result look convincing on the scoreboard when he dotted down in the final minute.
"Perhaps we didn't match them early on which gave them just a little bit of confidence in that area... it made for a tough night," Read said.
"It took time but I felt we got to where we needed to be."
Hansen pointed out that players such as Dane Coles had shown huge growth during the series and said the addition of Sam Cane and Cruden to the leadership group signalled their coming of age as Test players.
He was also pleased with the effort of debutants Steven Luatua, Charles Piutau and Matt Todd, who boosted the team when they entered the match at a time when the All Blacks were under immense pressure.
"We can sit here and be frustrated with our performance because it wasn't our best. But at the end of the day when you look at the whole package I think we're going to go away and say we're okay," Hansen said.
"We've given ourselves a pass mark but (we have to) keep working."