Argentina hit back in reply with tries from Gonzalo Tiesi and Juan Manuel Leguizamon while two penalties from Felipe Contepomi kept it tight.
The two clash next in Mar Del Plata and Parks believes a maiden Test series win in the southern hemisphere will hinge on relying on him less.
"I think we got ourselves in space but credit to Argentina's defence which was very good," said Parks.
"I think we created opportunities but it was just a shame that we couldn't go to the try line. We'll look at that end and with a little luck we will score some tries."