"They were sharp, no doubt about it, there's a reason they were undefeated this year.
"We were pleased with the result and great to see some players take an opportunity that they were afforded, players that we know have got potential take another step in the right direction."
Hay wasn't totally content, saying the goal conceded was "sloppy" and levels dropped in the final 25 minutes as Algeria finished strongly.
"We didn't look like we were going to concede," said Hay. "We were pretty good for 65-70 minutes in terms of controlling the game but we switched off mentally, a little bit of fatigue as well. But we managed to hold on and grind out a win which is another good thing for us to be able to learn to do."
The All Whites took a 16th-minute lead through Andre De Jong. A clever switch of play from Marko Stamenic gave Francis De Vries space on the left flank, and his good ball allowed De Jong to head home after losing his marker with a well-timed run.
New Zealand doubled their lead just after halftime, through Callum McCowatt.
A neat interchange of passes culminated with De Vries driving into the penalty area, before he was brought down. The referee declined the penalty appeals – Hay said the foul appeared to be inside the box – but McCowatt dispatched the free kick with aplomb.
The Algerian side got a goal back in the 68th minute, as they began to get in behind the New Zealand defence.
"It was disappointing," said Hay. "It reminded me of the Curacao game. We were up 2-0, comfortable and cruising and then a catalogue of errors. But that's the point of these games, to find out a little bit about ourselves."
As expected, Hay made several changes from the last outing against Bahrain in October, with Tommy Smith, De Vries, Matthew Garbett, Elliot Collier and De Jong all starting.
Michael Woud was in goal, behind a back three of Michael Boxall, Smith and Nando Pijnaker. Kelvin Kalua and De Vries were the wing backs, with McCowatt, Garbett and Stamenic in a midfield triangle and De Jong and Collier leading the line.
"It was great to give some of the boys who haven't had much of an opportunity in the previous games a chance - they did well," said Hay, who was particularly impressed with De Vries, Garbett and Stamenic.
"[It was] good to get another win but we know there were a number of areas we need to look at ahead of the Gambia game. That's what we'll be working on over the next couple of days."
All Whites 2 (Andre De Jong 16', Callum McCowatt 49')
Algeria A 1
Halftime: 1-0