As Holland took themselves to the brink of elimination from Euro 2012, on Wednesday picked off by Germany's precise counterattacks and the suddenly lethal finishing of Mario Gomez, it was difficult not to attach a measure of significance to the jerseys in which they played, a quartered design featuring two shades of the traditional orange. One for the starting players and the other for the moaners, presumably.

On the eve of the match Wesley Sneijder had made public the existence of yet another split in the eternally fissiparous Dutch ranks, and although it was not necessarily visible in their performance, it can hardly have helped their effort to stay in the tournament.

"It's time we let go of these pathetic egos," he had said in a poorly timed outburst. "If somebody is creating a mess, I will stand up against them. We don't need a psychologist with the Dutch team. We are grown-up men. The ones who have a problem with other players or the manager should tell them face to face. That is the only psychology we need. We have to stop living on little islands. We must all go for the same goal or face the consequences."

The old story, in other words. And if he was right, Holland are in danger of paying the price once again after next Sunday's final round of matches in Group B. Unlike 1996, when a 4-1 thrashing by England exposed splits along racial lines, this time the divide seems to be between those enjoying the favour of Bert van Marwijk, the head coach, and those left to kick their heels on the bench.

Principal among the latter was Rafael van der Vaart, the Tottenham player who was vying with Sneijder for the playmaker's role. "I am very disappointed," Van der Vaart told a Dutch magazine. "The coach has his preferences, I am not part of them and I don't think that is going to change. I will continue to give 100% but at the same time I have the right to express my disappointment."

No you don't. To believe that a player has the right to go public with such complaints in the middle of a tournament might be said to be the quintessence of Dutchness, or at least typical of the complex psychology of the Dutch footballer: a belief that he is always right, and that only his opinion matters, but – strangely – that by expressing it he is doing nothing to corrode the collective effort.

Needing a win to ensure the four teams in Group B finished the second round of matches with three points apiece, Van Marwijk's chosen XI started with a promising display of aggression. For a while it even looked as though Robin van Persie was going to establish himself – rather belatedly, at the age of 28 and with more than 60 caps – as an international player of substance.

Abetted by the busy Sneijder and Arjen Robben, he found himself in several promising positions but failed to take advantage of his early opportunities. In the second minute he took a return pass from Sneijder but fell over near the penalty spot, five minutes later he controlled Mark van Bommel's long ball over the defence quite beautifully but failed to beat Manuel Neuer, and in the 11th minute he ran on to Robben's excellent pass down the inside-right channel but screwed his shot wide. A further five minutes later, when Johnny Heitinga launched another long diagonal, he accelerated towards goal but could not escape Jérôme Boateng's tackle.

After that Gomez took over, inspired by the cool-headed passing of Bastian Schweinsteiger. With Holland two goals down at the interval, Van Marwijk chose to bring on his other central striker, Klaas-Jan Huntelaar, moving Van Persie out to the wing. Van der Vaart was the other arrival at the start of the second half, taking Van Bommel's place as well as the armband.

The Spider, as Metallist's stadium is nicknamed, features a running track, but their distance from the playing surface did nothing to diminish the ardour of the two sets of supporters, although the balance tilted during the course of the evening as the German fans glimpsed the outline of future champions while the Dutch feared that they were looking at the ghosts of the side they hoped to be cheering to another final. Then it tilted back again.

Gomez had been off the field less than a minute, replaced by Miroslav Klose, when Van Persie brought the game back to life midway through the second half with the sort of goal familiar to his fans in north London. Cruising across the face of the penalty area, he chose his moment to unfurl a quite majestic shot from the edge of the D, leaving Manuel Neuer helpless as the ball whistled past his dive.

Joachim Löw's side had suffered for the sin of taking a foot off their opponent's neck, but Holland deserved credit for their persistence. Before Van Persie struck he had brought a flying save from Neuer, while Sneijder fired one drive past a post and had another bravely blocked by the flying Boateng. Whatever the internal problems, they were not going down without some sort of demonstration of their quality, but they will need some luck if they are to turn two defeats into a platform for progress to the quarter-final.