England scored four tries through Joe Launchbury, Billy Twelvetrees, Chris Ashton and Ben Morgan but it was a patchy performance which lost momentum in the second half.
And Lancaster admitted the side, who beat Australia last weekend and have won nine of their last 10 internationals, would need to improve for next week's encounter against world number one New Zealand.
Lancaster said: "All the players are pleased overall but no-one is jumping up and down. We have a big game coming next week.
"Defensively we were excellent but game management is where we need to concentrate most.
"Win or lose next week depends on who manages the game best. Second half, clearly Argentina upped their game. We didn't quite manage the breakdown as well as we'd done in the first half, we were a little bit loose and Argentina kept the ball for long periods.
"We need to look at those areas and improve for next week. Overall, if you said that 31-12 was going to be the scoreline, I'd have taken it, definitely.
"Every international team is looking for that complete performance. You often see it from New Zealand, the top team, and that's what we're striving to get. We know we've got to improve in certain areas for next week but the positives far outweigh the negatives".
Lancaster admitted he had some big decisions to make for the All Blacks, not least the wing position where Ashton scored just his third try in his last 19 Tests, even though there were suggestions he was out of play when he grounded the ball.
Ashton, it was revealed, would not have been playing if Christian Wade had not injured a hamstring in training on Tuesday.
Lancaster said: "Christian was in at some point on Tuesday but he tightened his hamstring towards the end of training. Chris then came back into the equation.
"During Tuesday's training Chris' attitude was excellent, on Thursday his attitude was excellent and I'm pleased for him to get his try today. He enjoys scoring and it was nice for him to get that one."
Backs coach Andy Farrell was adamant that England needed to improve but also saw promise in their first-half display.
With one eye on the All Blacks next week, Farrell said: "We'll have to play better. We'll take some really good lessons from this game.
"I thought the first half we set the game up perfectly. We asked a lot of Argentina. They were hanging on by the skin of their teeth with the possession and territory we had.
"There were a few tries we left there but first half I thought the game was set up beautifully because we took the legs out of them.
"Second half we lacked a bit of patience. We forced one or two things.
"However, there aren't many teams that have out-mauled Argentina twice on the trot like we did and got over the line once and scored the second time. That's a massive plus for our forwards.
"There aren't many teams who have got so many penalties from scrums against Argentina."
Fly-half Owen Farrell kicked a penalty and three conversions and Toby Flood also landed a conversion in the second half, while Nicolas Sanchez scored three penalties for Argentina with Marcelo Bosch landing a long-range effort.
Lancaster said: "That's nine out of the last 10 internationals we have won so we have got an inner-confidence building but we recognise the challenges coming our way."
Argentina head coach Daniel Hourcade said: "In the first half we kicked the ball away too quickly so we let England dominate the play and in the second half we corrected that and managed to dominate the attack a bit more.
"We were more aggressive. When we started we were perhaps a bit nervous."
On Ashton's try, Hourcade said: "I think he was out of play. I don't think it was a try."