An Australia squad that had been savaged by fans and media alike after losing 4-0 to Germany, kept their World Cup hopes alive with a 1-1 draw with the Black Stars, despite having Harry Kewell red-carded for a goalline handball after 25 minutes.
"I think it was a fantastic performance from my players," the Dutchman said.
"We played 70 minutes with ten players. We knew we had to win to keep everything in our hands and we did everything to win the game. Even with ten men we had some great chances.
"I think we were very unlucky with the red card, which I think was a mistake by the referee but the players did a great job and now they have to do another one in four days time against Serbia."
Verbeek added: "We all know the Australian spirit. We are famous for that but still you have to show it.
"The players told me the whole week we will show everybody and they did."
Verbeek did not dispute that Ghana should have been awarded a penalty when teenage centreback Jonathan Mensah's fiercely-struck shot struck Kewell on both chest and forearm as he attempted to block the ball.
But he said Italian referee Robert Rosetti did not have to send the Australian forward off.
"What can you do with your arm? You cannot cut it off. It is a handball, it is a penalty. But as far as I know it has to be intentional to send the player off."
Verbeek admitted he felt for Kewell, who has played just a few minutes of football this year before taking the pitch here as a result of Tim Cahill being suspended.
"If you are working for six months to get to the World Cup -- and not a lot of players would have done what Harry did to be ready -- then you play and have to go out after 25 minutes - he will be devastated.
"But if we go to the next round Harry can play again, so let's stay positive."
Australia now have to beat Serbia in their final group D match, in Nelspruit on Wednesday, to have a chance of reaching the last 16. Realistically, given their goal difference, they will probably also need Ghana to beat the Germans.
Verbeek will have Cahill back from the final group match but Kewell will now be suspended alongside veteran centreback Craig Moore, who picked up his second yellow card of the tournament here.
"Serbia have one more day to recover than us but we have three days and this performance gives us a lot of confidence that we can do another great job against them," Verbeek added.
"It will be a difficult game but that is the World Cup.
"We will miss Craig but we have good players who can come in and do a job also.
"We have to go for it. We have to win this game. No discussion about it."
Ghana coach Milovan Rajevac praised Australia's spirited performance and said he was not too disappointed with his side's failure to capitalise on their numerical advantage.
"The result is quite good as well. Even if we had won the match we would have needed a point against Germany to go through.
"It shows that there is no game won in advance at the World Cup. All we can regret is having so many chances but not scoring. But that is football.
"Australia are back in the group and both they and Serbia will be going for a win in their final game."
Rajevac revealed that he expected to have experienced defenders John Mensah and Isaac Vorsah back for the Germany game after calf muscle and knee problems respectively kept them out of this game.
"We saved them today because we know the game against Germany is the most important for us. We will try to have them both healthy."
Rajevac is less certain about whether John Pantsil will be able to play against the Germans after the Fulham defender was stretchered off in the closing seconds of the match bleeding heavily after an aerial collision with Australian substitute Josh Kennedy.
Share
