Oranje endured a miserable European Championship in Poland and Ukraine, losing all three of their pool matches as they made an early exit despite possessing one of the strongest squads in the tournament.
Coach Bert van Marwijk has now departed with Louis van Gaal returning for a second spell.
And Inter Milan playmaker Sneijder believes he is already having a stabilising effect.
"At the European Championship we were not a team, now we are growing back towards being one," he said in De Telegraaf newspaper.
"That is necessary to perform. You see what we can achieve when we pull in one direction."
Sneijder offered special praise to Klaas Jan Huntelaar and Maarten Stekelenburg, both of whom were surprisingly left out of Friday's 2-0 win over Turkey.
Van Gaal had hinted beforehand he would choose Huntelaar over Robin van Persie to lead the attack while there had been no suggestion Stekelenburg would lose his place in goal to Newcastle's Tim Krul.
Dutch players have a history of making their feelings clear when not selected but both Schalke striker Huntelaar and Roma stopper Stekelenburg have kept their counsel.
"They obviously were very disappointed not to have been chosen but they have behaved," said Sneijder.
"With this coach it is obvious that no-one can relax and your chance may come faster than anyone expected."
Stekelenburg's absence may last just one game as he is poised to return for Tuesday's trip to Hungary with Krul ruled out due to an elbow injury.
The clash in Budapest will provide Netherlands with another stiff test in Group D.
The Hungarians won their opening game 5-0 in Andorra but Sneijder was in bullish mood.
"After four defeats in a row, the game against Turkey gave us the confidence we need," he said.
"To start a qualifying campaign like that, what more could we want?"
Hungary have not qualified for the World Cup finals since Mexico 1986 and Dinamo Moscow winger Balazs Dzsudzsak is determined to end that disappointing run over the next two years.
"Playing in a major tournament finals is a dream for all Hungarians," admitted the former PSV Eindhoven star to Voetbal International.
"As a footballer you want to appear at the highest level at least once in your career."
Hungarian football does, at least, appear on an upward curve with a number of its players now appearing in Europe's top leagues.
Dzsudzsak added: "That's a good thing.
"The Hungarian League is not good quality and the experience that our best players gain from playing abroad is of great value.
"It says enough that big clubs from leading leagues like Russia, England and Germany are sending their scouts to Hungary."