Shprygin was among a group of Russian fans expelled from France after violence flared before and during Russia's Euro 2016 match against England in Marseille.
New Zealand is now without a win in four trips to the Confederations Cup, and next plays Mexico on Wednesday in Sochi.
"The game didn't go how we wanted", he said afterwards.
With three points, Russian Federation will next face Cristiano Ronaldo's Portugal in Moscow on Wednesday.
With President Vladimir Putin in attendance and 44,000 tickets sold, today's Confederations Cup opener will give Russian Federation the chance to show off its preparations for next year's World Cup despite concerns over stadium security and infrastructure.More news: Putin says US sanctions will 'complicate relations'
Control matches before the start of the Confederations Cup for New Zealand were not easy, and the meeting against Northern Ireland and Belarus ended in defeat with the same score 1: 0.
Shprygin, who had been deported from France past year during the European Championship, said he had been notified by Confederations Cup organisers that his fan-ID, needed to attend matches, had been cancelled. Portugal and Mexico are other teams in Group A and will face-off on Sunday, June 18. It came off some lovely passing from the hosts, with Glushakov lifting the ball over the goalkeeper and off the right post while a insane scramble at that post took place.
It helped the Russian team to seize the lead after twice having shots stopped on the line.
They all slid in at the same time but the ball dribbled into the net and was awarded to Boxall as an own goal.
From Russia's fourth corner, defender Viktor Vasin's header saw the ball spin off a post and across the goalmouth before Michael McGlinchey cleared.More news: Trump Confirms Being Investigated for Firing Ex-FBI Director Comey
When the goal came, it had an ugly finish after two pretty pieces of individual skill once the All-Whites defense needlessly lost the ball.
New Zealand had their first major chance in the 78th minute.
Both teams were lined up on the pitch for an unusual pre-match protocol, looking up at the VIP boxes to hear from Russia's leader and FIFA President Gianni Infantino, before being able to complete their preparations.
The hosts continued to crank up the pressure after the break, forcing the impressive Marinovic into a fantastic double save, but Russian pressure finally told when Krasnodar striker Smolov - top scorer in the Russia Premier League for the past two seasons - tapped home from an Aleksandr Samedov cross on 69 minutes.More news: HUD Secretary Ben Carson: Give Robert Mueller a chance on Russian Federation probe
- German minister sees hope of 'soft' Brexit, with conditions
- Trump not under investigation, says lawyer
- Euro zone yields off lows as US policymakers hike rates again
- Amir, Fakhar lead Pakistan to Champions Trophy triumph
- Arsenal in contract stand-off with Alexis Sanchez and Alex Oxlade-Chamberlain
- Bogaerts hits 2 homers to lead Red Sox over Astros 6-5
- Champions Trophy final: India opt to field against Pak
- Protests Following Afghan Blasts Call for Security Chiefs to Step Down
- Newt Gingrich: Trump has a 'compulsion to counterattack'
- Cosby prosecutor undeterred by mistrial, vows to try again