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Bert van Marwijk lamented Australia’s lack of luck but was still looking on the bright side as his short reign as Socceroos coach came to a bittersweet end with a 2-0 defeat to Peru on Tuesday.

Appointed in January and out of a job now that their tournament is over, the coach praised his team and said the country should have its “heads up” despite finishing bottom of Group C with only one point.

Van Marwijk said a lack of good fortune and some poor officiating was to blame for Peru’s 2-0 win, their first World Cup victory in 40 years.

“We are not lucky, because the first goal in my opinion was offside, and the second goal was a very lucky goal, so we don’t have luck in all three of the [group] games,” he told a news conference.

“We played against France, Denmark and now Peru, and I think in all three of the games we gave a good performance, and this team has really improved from the day I started working with them.”

Ultimately it was a lack of firepower that stopped the Socceroos from progressing. Van Marwijk finally introduced veteran Tim Cahill off the bench, but the talismanic 38-year-old couldn’t add to his five goals in his three previous World Cups.

“Against France, in football we were at least equal with France, and with Denmark even better, and today I have the same feeling,” Van Marwijk said. “But in all three of the games, we couldn’t make a difference in goals. That’s something this squad misses on this level.”

Van Marwijk’s exit, after a five-month contract following Ange Postecoglou’s resignation, leaves with no regrets as Graham Arnold will become Socceroos coach with January’s Asian Cup in his sights.

“I loved to work with Australia and the players, but I’m also very happy that I’m free again,” he said.

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