"It is impossible to play better than we did today," Pellegrini said.
Tottenham is languishing in ninth place despite spending more than 100 million pounds (now $160 million) on mostly attacking talent in the summer. And with Manchester United up next weekend, they could yet find themselves even further out of the title picture in a season that had initially promised so much.
With just nine goals in 12 league games, scoring has become a serious problem since the summer departure to Real Madrid of Gareth Bale, who saved them so often last season. Not since a 7-1 loss to Newcastle in December 1996 have they been beaten by a six-goal margin and it could have been a lot worse.
City, meanwhile, remains the enigma of the season. Flawless in six matches at the Etihad, they have picked up just four points so far from a possible 18 on their travels.
As so often at home, City exploded out of the traps Spurs midfielder Sandro was sick on the pitch, such was the intensity of the opening minutes and had the game sewn up at halftime. And the hosts were given a helping hand by Tottenham goalkeeper Hugo Lloris.
Spurs' approach is to play the ball out from the back through the France goalkeeper but the tactic backfired here before many fans had settled in their seats.
Lloris' weak clearance went straight to Aguero and although Lloris saved the Argentine's curling shot, the ball fell to Navas, who curled a clever shot over the keeper into the top corner for City's fastest ever goal in 21 seasons of the Premier League and the second quickest this campaign.
"It was a difficult start for us," Villas-Boas said. "After that, everything you had in mind goes down the drain."
Spurs enjoyed some early possession, with Erik Lamela having a shot cleared off the line by Martin Demichelis, but they always looked vulnerable at the back and Lloris was at his best to deny Aguero chipping in for the second after seven minutes.
Lloris was his own worst enemy for the second goal too, making another tame kick to spark a City attack that saw Samir Nasri feed the ball to Aguero, whose effort was parried away to Negredo. The Spain striker's volley from eight yards deflected off Younes Kaboul onto the leg of Sandro and into the back of net.
Aguero wrapped up a perfect first half for the hosts by steering in a textbook cross from Navas and Spurs were on their knees. It was to get much, much worse.
Yaya Toure had cantered through the first 45 minutes but he burst into life in the 50th by exchanging passes with Negredo and storming into the box, where he crossed unselfishly for Aguero to sidefoot home for his 15th goal in 13 games.
"For me, Kun (Aguero) is just after (Lionel) Messi and (Cristiano) Ronaldo as one of the best three players in the world," Pellegrini said.
Nasri toe-poked against the bar before Negredo span his marker from Fernandinho's through-ball and fired a brilliant finish into the top corner. 5-0 and still more than half an hour left.
Mercifully for Tottenham, Aguero and Nasri were taken off soon after the hour mark but the introduction of forgotten man Emmanuel Adebayor for his first appearance of the season failed to spark Spurs.
And after starting the rout, Navas finished it after more dreadful defending by Spurs. A raking pass by James Milner failed to be cut out by Jan Vertonghen and Navas ran through to slip a finish past Lloris.
