Wales make the trip to Belgrade facing a four-point deficit to Sunday's opponents and Republic of Ireland, meaning that Chris Coleman's side cannot afford defeat this weekend.
They are clear underdogs due to the absence of the suspended Gareth Bale, but Gunter has insisted that they possess enough quality to return with a positive result.
The 27-year-old is quoted by BBC Sport as saying: "We have shown in the past in big games we can go and win matches people think we probably can't.
"We are in a situation where we have to go to Serbia and perform and pick something up.
"If we go and play as we have done over the course of the last two to three years, we give ourselves a really good chance."
The two nations played out a 1-1 draw in Cardiff in November.