The former international last month signed a three-year deal to become head coach, with a remit of creating a winning team whilst developing young talent.
Southgate has spoken of his desire for the team to play with freedom and he got that this evening as England peppered the Moldova goal.
While debutant Saido Berahino's early strike was all the Young Lions had to show for their endeavours, Southgate was pleased with what he saw.
"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 punchline at the end 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 2 v 1 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."
The match came just a day after Football Association chairman Greg Dyke's hard-hitting speech bemoaning the current state of the national game.
Southgate insists it was not on his mind this evening and was not nervous in what was his first match back in management for nearly four years.
"I was just really looking forward to seeing the players transfer what they've been doing in training," he said. "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."
The new era came in the wake of a miserable summer in which England lost all three matches at Euro 2013, leading to the end of Stuart Pearce's six-year reign.
"We have kept in contact right through and he has been very supportive," Southgate said of his former international team-mate.
"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."
Pearce led the Under-21s to four successive European Championships, with Southgate charged with making it five.
Next up for his side is a trip to Finland on Monday, when Berahino could well start again following his match-winning debut at the Madejski Stadium.
"They were brilliant defending but we won the game," the West Brom striker told BT Sport.
"At least we created a lot, that's a positive sign, but we've got to make sure we put them in against Finland.
"Gareth Southgate has been great, he's come in and introduced us to what he wants us to do.
"We prepared really well for this game and now we've got to concentrate on the next one."
- Sports & Recreation
- Gareth Southgate
- Saido Berahino