To earn such praise from the Frenchman, who is not backward in coming forward with expressions of impatience or despair with fellow team members, Armstrong had given a convincing demonstration of goalscoring instinct in the space of 20 minutes to decide a contest which appeared to be heading for a stalemate.
After 62 minutes he followed in a chipped pass from Darren Anderton and rounded Everton's keeper, Thomas Myhre, before shooting Tottenham into a 2-1 lead from an acute angle.
Having got his eye in at last, after a number of hesitant efforts in the first half, Armstrong was clearly on a roll. And when Tottenham's promising central defender Luke Young drilled the ball through the heart of the Everton defence to send Armstrong in on goal with his striking partner Les Ferdinand, goal number three was clearly imminent. A neat backheel by Ferdinand then sent Armstrong clear of the last defender and free to drive home a powerful shot.
Armstrong completed the first Tottenham treble since Jurgen Klinsmann rounded off last season with four goals against Wimbledon when he was sent clear on the right by Anderton's pass. Jubilation for Tottenham; desperation for an Everton side who had seemed equal to their challenge.
Walter Smith criticised a linesman and referee Graham Poll for allowing Armstrong's first goal. "It was a clear handball and that's why our goalkeeper Thomas Myhre hesitated in going for it," said the Everton manager.
None of Smith's charges seemed up to the task of containing Ginola, who sent over a sequence of sumptuous crosses from the left. However, Armstrong was unable to use the service to best advantage, most notably in the 19th minute when he miscontrolled a floating offer at the far post.
But Tottenham's frustration ended within four minutes, as an Armstrong header from another Ginola cross spun down off the back of a defender's head and Ferdinand, given sufficient time and space to run back behind the ball, jabbed it powerfully past Myhre on the turn.
Compared to their dismal home record of six goalless draws and three goals in 10 matches, Everton's away form this season has been positively bountiful. In the nine matches before this one, they managed an average of a goal a game.
The average was duly maintained on the half hour when Don Hutchison's cross was headed low past the Tottenham keeper by Ibrahima Bakayoko.
Goals: Ferdinand (24) 1-0; Bakayoko (31) 1-1; Armstrong (63) 2-1; Armstrong (76) 3-1; Armstrong (81) 4-1.
Tottenham Hotspur (4-4-2): Walker; Carr, Young, Campbell, Sinton; Fox, Anderton, Nielsen (Clemence h-t), Ginola; Armstrong (Iversen, 88), Ferdinand. Substitutes not used: Baardsen (gk), Calderwood, Edinburgh.
Everton (3-5-2): Myhre; Unsworth, Bilic, Short (Cleland, 6); Ball, Collins (Oster, 76), Dacourt, Hutchison, Dunne; Barmby, Bakayoko (Cadamarteri, 32). Substitutes not used: Simonsen (gk), Grant.
Referee: G Poll (Hertfordshire).
Bookings: Tottenham: Ferdinand. Everton: Cadamarteri, Hutchison.
Man of the match: Armstrong.