Captain Chris Robshaw and fly-half Owen Farrell scored second-half tries as England overturned a 13-6 deficit.
"We stayed patient, didn't chase the scoreboard, built pressure and deserved the win," Lancaster told BBC 5 live.
England delighted by 'great' victory
"You never know how youngsters playing for the first time at Twickenham are going to deal with the situation but I was delighted with their maturity."
Centre Joel Tomkins was making his full international debut, number eight Billy Vunipola his first Test start and Marland Yarde his Twickenham bow.
"Billy controlled the base of the scrum really well, he wasn't fazed by the occasion," Lancaster added.
"Marland showed power and physicality and was enthusiastic to get his hands on the ball and Joel defended really well at 13."
Lancaster also praised England's overall defensive effort, despite Chris Ashton and Billy Twelvetrees missing tackles that led to Matt Toomua's first-half try.
"Any lapses put you under pressure and good sides capitalise on them so we'll have to look at that. But overall they worked hard for each other and they worked hard for the shirt.
"Sparked by the coruscating running of full-back Mike Brown, aided by two benevolent decisions from the match officials and powered on by two pieces of opportunism from skipper Chris Robshaw and fly-half Owen Farrell, England turned a seven-point deficit into a seven-point lead and then controlled the remaining minutes with muscular force."
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