"We believed we were fitter than them and we believed we could put them to the sword in the last 20 minutes. That was the case, but we just couldn't get over the finish line," said Jenkins.
"It was frustrating to lose our first game and we need to pick ourselves up this week and look forward to the game on Saturday - and another chance to win as a Lion. Hopefully we know a bit more about them now and we can get a result."
The Lions'problems at the scrum were on the opposite side to Jenkins, where 'The Beast' got on top of Phil Vickery. It meant the Lions were always playing catch-up after falling 12 points behind in the first half and then 19 early in the second.
"We just didn't play enough rugby in the first half and the Springboks got too far in front of us. Even though we finished very strongly it was just too much of a gap to catch up," admitted Jenkins.
"Decisions went against us on the right hand of the scrum and I'm not too sure what was happening. I had my head down on the other side but I'm sure we will look at the video and see what happened there.
"It is frustrating to be on the wrong end of the result because they didn't play much rugby. They just kicked the ball, although to their credit whatever they did do was effective.
"It was a great occasion and I couldn't believe the amount of red jerseys in the crowd. It was great to see all that support out there and I really enjoyed the occasion, but it was just a shame not to get the victory."