The Springboks face England in Saturday's final and Wales take on New Zealand in Friday's bronze game after losing 19-16 in Yokohama.
Gatland said: "It was a very tough encounter, and well done to South Africa. We punched massively above our weight in terms of playing numbers in Wales, we gave 100% in a close contest.
"But South Africa deserved to win."
Handre Pollard's late penalty sealed victory for the Springboks after Wales had hit back with a Josh Adams try to be 16-16 going into the final minutes.
Wales captain Alun Wyn Jones said: "We showed it today, stayed in the arm wrestle and stayed in it and I was proud of us when we went 16-16, but we piggybacked penalties down the park and South Africa took advantage so congratulations to them.
"Today we fell short. Hopefully we'll get another opportunity it wasn't our day, but I'm still proud to pull this jersey on and represent all the people in red in the stadium."
Wales have fresh injury worries going into their game against the All Blacks.
Jones' fellow lock Jake Ball Jake Ball said: "Everyone's worn their heart on their sleeves in that game, the boys have put in a hell of an effort, we just have to look back on it, it's just disappointment at the moment to come so close.
"Maybe we didn't have the swing of things in that last 15 minutes, but it's hard to put it all in words at the moment, just disappointed.
"All the boys are down, there is one game left and it's just how we go about using that for motivation for this final game."
Fresh injury worries for Wales
George North limped off with a suspected hamstring injury and prop Tomas Francis suffered an arm injury in another bruising contest.
Jones' fellow lock Jake Ball Jake Ball said: "Everyone's worn their heart on their sleeves in that game, the boys have put in a hell of an effort, we just have to look back on it, it's just disappointment at the moment to come so close.
Maybe we didn't have the swing of things in that last fifteen minutes but it's hard to put it all in words at the moment, just disappointed.
All the boys are down, there is one game left and it's just how we go about using that for motivation for this final game.