The hosts scored three tries in the first half, but were able to add just seven points after the break.
The England captain told Sky Sports News: "We came out all guns blazing and got off to a flying start with a couple of tries. Unfortunately Argentina had a bit more impetus in the second half and put us under a lot more pressure
"We need to look at ourselves going into next week and make sure we're switched on and ready to play. We're looking forward to it. We'll focus and we'll get it sorted.
"New Zealand [who play England next Saturday] is always a tough challenge. We've had two tough Tests and come through them with positives and areas to work on."
England have registered back-to-back wins in the Autumn Internationals following their victory over Australia last weekend.