Baxter came under fire with those reverses - particularly the back-to-back defeats to Cape Verde - as South Africa finished bottom of their qualifying group and again missed out on a World Cup.
Bafana, who also failed to qualify for the 2017 Africa Cup of Nations, are now hoping to put the long-suffering public out of its misery by qualifying for the 2019 AFCON in Cameroon.
Bafana made a bright start to their continental quest by beating Nigeria 2-0 in Uyo in Baxter's first match in charge since returning to the national team hotseat at the expense of Shakes Mashaba.
His men next host Group E leaders Libya at Moses Mabhida Stadium in Durban today (15h00). The north Africans thumped Seychelles 5-1 in their qualifying opener.
"That is one scenario, [using skillful players to] pick our way through a very compact and carefully lined up Libya side," Baxter said.
"It's a new coach and he's going to look at other games. Maybe he's going to look at the matches against Senegal of how they frustrated us, and even Cape Verde [on how] they frustrated us, and think 'Hey, that's the way to go'.
"Well, we've worked on that, we've worked on that. I do believe that we can be patient. I think the crowd is going to be patient if it's like that.
"I watched Germany against France (in the UEFA Nations League in Munich on Thursday); Germany were frustrated by France and the crowd stayed positive and I think that's going to be important for us.
"The crowd has to stay positive and if they do that I think we can pick our way through. I think once they have got to come out at us spaces open up. I think that'll be an advantage for us."
With Bafana's last appearance at a major tournament occurring at the 2015 AFCON in Equatorial Guinea, Baxter is well aware of what is expected of the team.
"My major, major motivation is to give the people of this country a major tournament to be involved in," said the former Kaizer Chiefs mentor, whose first tenure as Bafana coach ended in 2005 after the nation fell short of reaching the 2006 World Cup in Germany.
"And then we can discuss the personal gains and the benefits or kudos. But for me I've got no thoughts of that at this moment. With this game we can move closer to what we want to achieve."