The Three Lions had to wait until the 81st minute to find their winning goal, with substitute Harry Kane heading home after mounting pressure from England.
And the Head Coach was always confident that his team would make a breakthrough after enjoying the vast majority of possession and chances against their hosts.
Lithuania 0-1 England
UEFA European U21 Championship
Group One Qualifier
Friday 5 September 2014
Dariaus ir Gireno Stadium, Kaunas
"I think we expected a difficult game because we knew Lithuania would defend deep and would get numbers behind the ball, which is a problem we’d faced quite a lot in this group," he said.
"But I was pleased that we were patient.
"In the first half, we weren’t quite patient enough but we knew if we kept passing the ball that in the end, the opposition would tire and we’d get more chances.
"So I was pleased with that and the way our midfield players played off each other.
"We think we had another gear to go into, and we spoke at half time about what the opposition wanted us to do, which was to get frustrated and try to force things and then switch off.
"We slightly got caught up in that, but I thought we did well and we just need to show a bit more quality around the penalty area with our final ball or final cross and to make sure that we keep concentration at the back.
"In the second half, we certainly did that and had three or four really good chances."
Lithuania weren’t without their opportunities to cause an upset though, particularly in the first half, but once Southgate made a few changes to pose a different threat, the opportunities arrived.
"We conceded two or three chances which were of our own making, so we need to do better there," he added.
"But the beauty of us having a strong squad was evident as we were able to make a few changes just to offer a different problem.
"We were well worth the win, but sometimes it has to be that you wait until late on in a game to break teams down so in terms of an away performance I’m very pleased with the way we went about our job.
"I liked the way we managed the game as it wore to its close as we had to deal with a couple of long balls and set plays into the box, but we saw the game out well which is another lesson that we took from last summer.
"It’s been a pleasing few day’s work really."