Kris Commons scored the only goal 13 minutes from time and, although it was not a vintage performance from the Scottish champions, Lennon said it was the kind of result he was looking for beforehand.
"I am delighted with the performance and the result," Lennon said. "They made it difficult for us to break them down but it was not frustrating, it was understandable.
"We weren't at our best but that was always going to be the case, there is still a bit of rust there. We still have a lot to do in the tie but we are confident.
"The crucial thing is the clean sheet. That is important. If we score over there Elfsborg have got to have three. The tie is probably in the balance but we are confident that we can go there and get a result.
"The Astroturf might change things with the way I pick my team. But I was pleased with the result. I would have taken 1-0 before the game."
Commons felt Elfsborg treated them much in the way his own side had tried to prepare to face Barcelona last season.
He added: "It reminded me a lot of how we played against Barcelona. We had to give their top-quality players respect, get behind the ball and make us break them down.
"In fairness to them, they probably saw how good we are at home and gave us respect. They would have been happy at 1-0.
"It could be a vital goal in the grand scheme of things but I do think we can score in Sweden. Fraser (Forster) could have stayed in the changing-rooms. I don't think the ball touched his gloves.
"They were happy at 1-0. I think they would have been delighted at 0-0. But we are more than confident about going on the road and getting goals."