Spain took a few minutes at the end of its breathtaking Euro 2012 triumph to prove it is human, after spending the previous 90 showing why, in soccer terms at least, it is anything but.

A 4-0 victory over Italy on Sunday clinched an unprecedented third straight major tournament success for the majestic Spanish, many of whom brought their young children onto the field at the final whistle to celebrate with them. It was a touching gesture and spawned lovely scenes of childlike exuberance, with the kids hugging and playing excitedly with their delighted fathers.

Yet for the previous couple of hours, those smiling adult faces in red uniforms had shown sporting ruthlessness of the highest order to silence a growing band of critics with a display of soccer magnificence.

All the accusations of boring play were washed away at the Olympic Stadium in Kiev as Italy, having shown so much spirit and resilience in reaching the final, were simply picked apart with a thousand cuts.

Just as it had all tournament long, Spain controlled the ball, dominated midfield and strung together pass after pass. This time, though, the old attacking intent was in place again after seemingly disappearing during the early part of the tournament.

David Silva got the first goal after only 14 minutes. His header came at the end of an outstanding move that saw Cesc Fabregas cut the ball back from the touchline for a goal of technical excellence. From that point on, it was all one-way traffic.

Spain's second goal was perhaps even better. Left back Jordi Alba charged nearly the full length of the field to collect a pinpoint pass and deliver a cool-headed finish.

When an injury to Italy’s Thiago Motta forced him from the field – after his side had already used all three allocated substitutes – Spain was able to run riot even more. Late replacements Fernando Torres and Juan Mata both got on the scoresheet to cap off a spectacular display and send the discussions of "greatest team ever" into overdrive.

Comparing teams from different generations is always a fool's errand, but this Spain side fully deserves its place at the very forefront of the conversation. It is incredible to think that its success at Euro 2008 ended a drought of 46 years since the nation’s previous major success. Now it has a pair of Euro titles with a World Cup sandwiched in between.

International soccer has never been more deep or diverse, but Spain makes the opposition look second-rate, seemingly at will. In 10 straight knockout games in tournaments, the Spanish have not conceded a single goal and yielded just one in its six matches at Euro 2012.

And to think that people had started to doubt them. Going into the competition, it was felt that the supposed rift between the rival players of Real Madrid and Barcelona would be destructive. Speculation also focused on Spain's dwindling motivation after so much former glory.

[More Euro 2012: Antonio Cassano overcomes stroke to help Italy make surprising run]

Not so. Silva, Manchester City's star playmaker, was the only player not from Madrid or Barca to start the final for Spain. Moreover, this was as seamless a blend of teamwork as you could ever wish to see.

Some key members of the team, such as goalkeeper Iker Casillas and midfield general Xavi, are not getting any younger, and a few fresh legs might be needed for the World Cup in 2014. But this is not a team that is weakening with age or one that is even close to the end of its road. No, it is one that has figured out the blueprint for winning on the biggest stages of all and is enjoying putting it in place.

The 1-0 wins over Germany in the Euro 2008 and the Netherlands at the World Cup were wars of attrition – fierce battles that had to be survived not seized. Sunday's victory, instead, was a festival – a celebration of a truly great team and a dynasty that shows no sign of ending.

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