Century-maker Smith collapsed and lay prone on the ground for several seconds before staggering to his feet.
After he was given the all-clear following medical attention he continued his stand as Australia closed in on New Zealand's first innings 370 in the second Test.
The danger of head blows has been highlighted since Australian Phillip Hughes died after being struck on by a bouncer 15 months ago.
"It's never one's intention to hit someone in the head and see him go down like that.
Also Read
Wagner, New Zealand's go-to bowler to break stubborn partnerships with his use of the short-pitched ball, defended the bouncer as an effective weapon.
"Short-pitched bowling is just about trying to throw them off their game and try to get a wicket in some sort of way," he said.
Wagner used the delivery to good effect late on the second day by removing Joe Burns for 170 and Smith for 138 to have Australia 363 for 4 at stumps.
Both went in similar fashion as they tried to pull down short-pitched deliveries and hit the ball to Martin Guptill at square leg.
Being New Zealand's enforcer is not Wagner's normal role but "is something that gets given to me and I love doing any role that is given to me," he said.
"Obviously the two wickets at the end helped us and were quite crucial."
Burns, who bounced back from scoring nought in the first Test to produce a career best 170, was in partnership with Smith when the Australian captain went down and said it was a disturbing feeling.
"It certainly always a concern when you see someone get hit in the head, it got him quite flush as well," Burns said.
Australia go into the third day of the Test on Monday in a strong position just seven runs behind New Zealand and with six wickets in hand.