After a tough few days in which the players have had to deal with the news they were not required for the first Test against the All Blacks, Jenkins was happy for the Lions to emerge victorious.
After a blistering start thanks to Gavin Henson's first try, the Lions lost their cohesion at times.
However, Jenkins stressed: "The most important thing as far as we were concerned was to actually win and we did that.
"We started particularly well, maybe too well. We became too individual far too early in the game and to be fair to Southland they recognised that and what they did was front particularly well.
"They got into us and in among us, and they have taken advantage of maybe a lack of cohesion in our performance and we've ended up having a particularly difficult game and we've made pretty hard work of it.
"But as far as we're concerned we'll take the win. It has been a demanding four or five days on this particular group of players and I think we've done particularly well.
"We won't be disappointed with them. In fact we've applauded them tonight in the way they have actually fronted up."
Skipper Michael Owen also praised the character of his team but conceded that at times they may have tried too hard to force the game, making errors which allowed Southland to stay in the hunt right until the end.
"It was tough for the boys," he said. "We started really well in that first 10 minutes; it was just unfortunate that we couldn't keep it going because we played some really good stuff there.
"But we got a bit sloppy and were maybe trying too hard and we lost our way a little bit.
"I think it shows the character of this squad to grind out a win like that after a tough few days."