The win pushed Tottenham to within four points of Chelsea at the top of the Premier League table, with Chelsea set to visit Manchester United at Old Trafford on Sunday.
Spurs took an iron grip on the game against Bournemouth with two goals in the first 19 minutes from Mousa Dembele and Son Heung-Min.
"It was important for us to get the three points and we got the three points", he said after the match at White Hart Lane. 'Now, if they [Chelsea] fail, we will be there.
Redknapp admitted that while Spurs are firing on all cylinders right now, they will need a dramatic slip up from Chelsea to get their hands on the Premier League title.
Hull remains two points above the relegation zone after 11th-placed Stoke ended its four-game losing run with a win that was wrapped up by Xherdan Shaqiri striking into the top corner from 30 yards (meters) with 10 minutes remaining.
But Mourinho's fifth-placed team, four points behind fourth placed Manchester City in the Champions League qualification scrap, are unbeaten in their 21 league matches since that first painful loss to Chelsea this season."It will be tougher this time around". "We fought against everyone, but now we are focusing on fighting our opponents when we play".
Lampard, 38, won three Premier League titles as a Chelsea player and made 631 appearances, scoring 209 goals during a 13 year spell at the club.
"Overall I am disappointed with our defensive display".
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Kane played down his feat, insisting the only focus was on Tottenham maintaining the form that has seen them win seven consecutive top-flight games for the first time in 50 years.
"It was great to be back out there", Kane said.
The 4-0 thrashing of Bournemouth was Spurs' seventh straight success in the EPL and means that Chelsea is still looking over its shoulder.
"Then we spend time and energy on preparing ourselves to compete in the best way".
"Never give up. 3-0, 4-0 or 1-0, 2-0 - the team must forget the result".
He said: "I think it was hard for all of our team, not just Jack". It's the biggest test for us. I think today it's not important the gap we have with Arsenal."The most important thing is to do our job, try to win games and try to reduce the gap with Chelsea".
The Gunners have lost five of their last eight league games and Redknapp believes there is now a stark difference between the application of Arsenal and Tottenham players.
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