With only two wins and one draw to show from 30 matches over 109 years, Wales's record against the Springboks is their worst against any team in world rugby.
Welsh fans will point to the fact that one of those wins came in the teams' most recent meeting last November. Their only other triumph came in the match to officially open the Millennium Stadium in 1999, with the draw achieved back in 1970.
Jenkins said there is nothing to be learned from the 29-19 win that saw out the last century because the game has moved on in every way, but he did suggest that the more recent fixtures should give Welsh fans hope.
"We have come close an awful lot of times," the former goalkicker extraordinaire, now the side's skills coach, told reporters at Twickenham.
"We won in November against them and we should have won in Nelspruit in that second Test last year, but we threw it away after being 30-17 up with nine minutes to go and lost. It was quite hard to take.
"It just shows that when you play against any of the top sides in the world you have to play for the full 80 minutes. You can't switch off at any time -- you have to constantly be on the ball and on the money.
"If we bring our A-game tomorrow I'm sure it will be a fantastic match and there is no doubt it could go either way."
If Wales are to make it two in a row -- having lost the previous 16 -- then they will have to be more clinical than they were against Australia last week.
Despite the Wallabies having two men in the sin bin, Wales failed to take advantage in a stirring but ultimately pointless 12-minute onslaught and ended up losing 15-6.
"Without doubt, we should have scored a try in that period," Jenkins said. "You have to come away with points against 13 men.
"We have been through certain scenarios. There were overlaps that were clear and we didn't make the right decisions. I think if we are in a similar position tomorrow, we will put that to bed."
(Editing by David Goodman)
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