Southgate's men only had Saido Berahino's early strike to show for their efforts but they peppered the Moldovan goal and Southgate was keen to look for the positives after the 1-0 victory.
"I think that, when we watch the game back, there will be so many good things from it," he said.
"But obviously, when it is 10 minutes until the end and they are starting to put free-kicks in your box, you run the risk of there being a punch-line at the end which you don't want.
"I am very pleased with so many things, though. I thought we controlled possession well, even when the goal didn't come, we didn't panic.
"In the first half I think we needed to get more men in the box, more support up to Saido, and probably to get crosses in slightly earlier because we made overlaps, made two versus one situations and just needed to be a bit more ruthless around the box.
"That was the same in a different way in the second half, but there is lots I am very happy with.
"I was just really looking forward to seeing the players transfer what they've been doing in training and several of them played with that freedom that I wanted.
"There were one or two slightly nervy passes in the first half, but I think that was understandable with it being a new start, new players, and the expectation of winning comfortably."
Southgate has taken over from Stuart Pearce, whose six-year reign ended after England disappointingly lost all three of their matches at Euro 2013.
"We have kept in contact right through and he has been very supportive," said Southgate.
"He sent me a message before the game today and that sums up the man really. He's been a good friend and he is a special person."