Referee Felix Zwayer has come in for criticism from the Socceroos, who labelled the German’s performance a “stinker” after what they believed was a series of injustices in their 2-0 defeat to the USA in the World Cup match in Seattle.

The co-hosts’ second goal was awarded by the video referee, and it was contentious given what appeared to be an offside player in the proximity of goalkeeper Patrick Beach when he tried to recover from a misdirected shot.

The main grievance, however, was what they believed to be a string of non-calls during the match. Connor Metcalfe appeared to be tripped in the area and forward Nestory Irankunda was taken out off the ball by American defender Chris Richards. Several more players’ pleas to the referee during the match were ignored.

Irankunda said the team was unlucky. “If you look at how the referee was today, [there’s] not much I can say about that,” he said. Asked to elaborate, the forward’s criticism was more pointed.

“The ref was having a stinker today, but I mean it is what it is,” he said. “He was giving every call to the USA. I get it, but at the same time, we know there’s two teams on the field, so you have to give the calls both ways and he didn’t do that today.”

Coach Tony Popovic said the contest was not overly physical, but the whistle was inconsistent. “I thought the referee gave too many fouls away, in all honesty, he said. “Sometimes you didn’t have to do much to win a foul, and on the other occasions you you had to do a fair bit to get one.”

Despite the result, the Socceroos believe they can quickly correct their listing World Cup campaign.

Australia found themselves down 2-0 at half-time after being outplayed in the opening half. The result secures a berth in the knock-out rounds for the US, whose fans loudly celebrated progression from the group stage at full-time in the 68,000-capacity Seattle Stadium. But it leaves Australia’s campaign on the bubble ahead of their final group-stage match against Paraguay in San Francisco next week.

Captain Harry Souttar was downcast after the match and admitted it was a frustrating afternoon, but said the Socceroos know they can still progress to the last 32. “[The reaction] has got to be a positive one tomorrow,” he said. “We can look back at the game properly and take bits that we did well and that we didn’t do well – there’s a lot of them.”

A draw against Paraguay will almost certainly be enough to secure qualification as the second or third-placed team in the group, but the Socceroos will understand more about what they will need following the other Group D match later on Friday (Saturday AEST).

“We’re in that position where we know we can go through, if we get a result. So yeah, full focus and positivity has got to be [there] for that last game,” Souttar said.

The Socceroos worked their way into the contest in the second half, but were unable to find a way back into the match against an opposition who were hungry and composed.

“We didn’t start well enough,” Souttar said. “They were in our faces, we couldn’t keep the ball down, we were always trying to get in behind early, we just didn’t really show that composure that I think you think you needed. But the reaction was good.”

Nestory Irankunda and Connor Metcalfe – goalscorers against Turkey last week – came on during the break and were impressive, alongside Cristian Volpato who made his World Cup debut.

Midfielder Aiden O’Neill said the Socceroos “still believe”, and they can take positives into the clash against Paraguay after the second half performance. He said Volpato had a “massive impact”, as did the other substitutes, which helped turn around the match.

“The boss always talks about the belief in the squad and I think maybe in the second half we really truly believed that we would get back into it,” he said. “Maybe you could see that as on the field, and we gave everything. I think everyone can see that.”

Popovic could not fully explain the first-half performance. “I don’t know if it’s the occasion, but we looked sluggish, heavy legged, dull,” he said. “They won every duel, they won every second ball and when you do that, it makes it very difficult to get any, gain any momentum.”

He said the second half response was “outstanding” and gives a platform to take into the next match.

“We’ve got to accept what happened today, and I’m really delighted with the second half, to be honest, with all the players that came on, and the players that didn’t have a good first half,” he said. “It’s a World Cup. We move on to Paraguay and we’ll work hard to be ready for that.”