The match was Redknapp's second in charge since being announced as the successor to Juande Ramos.
And that view is supported by Juande Ramos, the former Tottenham boss who managed Real Madrid for six months from December last year.
Poyet, who won 26 caps for Uruguay, has been out of work since being sacked alongside manager Juande Ramos at Spurs in October 2008.
Under his predecessor Juande Ramos they had had picked up only two points from their opening eight games - their worst start to a season.
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The home side were being nullified by Liverpool and Juande Ramos brought on Guti after the break to add some guile to their sloppy play.
The win, Tottenham's eighth under new manager Juande Ramos, ensured the hosts' improvement under the Spaniard was clear for all to see at the Lane.
Lennon, 21, was in fine form in Sunday's 1-0 win over Blackburn, having struggled to start on a regular basis under former manager Juande Ramos.
Tottenham were bottom of the Premier League with two points from eight games when Redknapp left Portsmouth to replace Juande Ramos as manager in October 2008.
Juande Ramos was sacked as Spurs manager late on Saturday, with Redknapp officially confirmed as his successor last Sunday - just hours before their 2-0 victory over Bolton.
Defoe had failed to hold down a regular first-team place at White Hart Lane and was told he was free to leave the club by manager Juande Ramos.
The 27-year-old had been left out of the Tottenham team for recent games because manager Juande Ramos felt the Bulgarian was too distracted by United's interest in him.
The Frenchman was booked for a needless foul on Shaun Wright-Phillips and then hauled down Malouda moments later, shortly before being taken off by a sensible Juande Ramos.
Tottenham manager Juande Ramos, who has won this competition for the past two seasons with Sevilla, had been given the ideal start when O'Hara's goal strengthened his side's grip on the tie.
Madrid twice came from behind to draw level, but goalkeeper Iker Casillas' error in stoppage time gifted Villarreal the victory which leaves Juande Ramos' side eight points behind Barca with just two games left.
"If you said to Juande Ramos to get rid of all his top players and give him 'X' amount and say get to the Champions League last eight he would just laugh at you, " he suggested.
Meanwhile, Tottenham manager Juande Ramos is clearly intent on re-shuffling the squad he inherited from Martin Jol when he took over midway through last season with Blackburn linked with a move for England international goalkeeper Paul Robinson.
Then, despite publicly stating a desire to stay with Portsmouth for the remainder of his managerial career, Redknapp was handed the chance to join Tottenham and found the opportunity to replace Juande Ramos too good to turn down.
The summer signing of Brazilian goalkeeper Heurelho Gomes from PSV Eindhoven gave a strong indication that Robinson was not going to figure uner manager Juande Ramos -- and he has chosen to return north after starting his career with Leeds United.
And, despite resting several first-teamers with Tuesday's Carling Cup semi-final against Arsenal in mind, Juande Ramos could have been forgiven for a sense of bemusement at how his side were not five or six goals up at half-time, such was the hosts' dominance.
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