Bafana Bafana squeezed into the knockout round as the last of the four best third-placed teams in the pool stages having beaten minnows Namibia 1-0 and lost to Ivory Coast and Morocco by the same scoreline.
The performances have drawn stinging criticism from fans, many of whom wrote on social media that they hoped the team returned home to avoid further embarrassment before a place in the last 16 was sealed on Tuesday when Mali defeated Angola.
But Englishman Baxter believes a fixture against Egypt in front of 75,000 at the Cairo International Stadium on Saturday could be just the tonic for his team.
"It is a great challenge and one that the whole squad are looking forward," he told reporters on Wednesday.
"We have got this opportunity to play the host nation in a hostile environment and that is the time you want people to stand up.
"They (the players) want to go on and they have strong reasons to want to do it. They want very badly to get past this hurdle."
South Africa have looked poor in attack and this is the area Baxter will be concentrating on in the days leading up to the Egypt clash, rather than a complete change in tactics.
"I don't think I have to change anything, we just need to strengthen some things," he said.
"Our attacking play has not been at its best, but I think on the whole our defensive play has been very good. We need to add on to that a functioning attacking game.
"Against Egypt, I am guessing they will come at us, so there should be more space on offer. If we can up our attacking game 10-15 percent, we will be able to give them problems."
Baxter said the players were also aware that a number of them had not been at the level he would expect.
"I don't think mentally we have to lift them. They know they can do a little bit better and be more efficient."
(Reporting by Nick Said; Editing by Ken Ferris)
