Spurs look set to miss out on a return to Europe's elite club competition next season after fourth-place rivals Manchester City opened up a four-point gap with their win over Blackburn at Ewood Park on Monday night.
Dawson suffered the agony of watching his team-mates take part in six enthralling group stage matches in the Champions League while he was sidelined with an ankle ligament injury.
Frustrated: Michael Dawson was left disappointed after Tottenham were held to a 2-2 draw at home to West Bromwich Albion at the weekend
He hopes to enjoy a full season in Europe's top club competition next year and has promised the club's fans he and the Tottenham squad will give everything they have to make it possible.
'We want to be in there again next season,' the defender added.
'We qualified for it last year and that's our aim this year. It will be hard but we won't give up. There is still a long way to go in the chase and we have to keep fighting until the end.'
Spurs blew the opportunity to move level with Manchester City last week when they allowed the Baggies to steal a point through a late equaliser from striker Simon Cox.
Following Monday night's 1-0 win at Blackburn, Roberto Mancini's side are now four points ahead with five games to go - including their Eastlands date with Tottenham on May 10.
City slickers: Manchester City are four points clear ahead of Spurs after their 1-0 win over Blackburn on Monday
Dawson is desperate to play Champions League football next term after this year's debut season saw AC Milan, Inter Milan and Real Madrid come to White Hart Lane.
The first hurdle towards achieving that goal comes in Saturday's game at Stamford Bridge, where Chelsea will be looking to keep alive their slim title hopes with a victory.
Spurs have not won a game there since 1990, but Dawson knows they must beat the Blues to keep up with City.
'We were gutted on Saturday,' Dawson said. 'We dropped two points but we have to pick ourselves up and concentrate on the massive game we have coming up against Chelsea.
'We haven't won there for a long time but hopefully we can put things right.
'They will still think they are in the title race and they will want to win every game to try and win the league but it's no good looking at everyone else. It's down to our form and hopefully we will get a result.'
Same again: Spurs beat City to fourth spot last season with a win at Eastlands and Dawson would love a repeat this term
Spurs secured Champions League qualification with a victory at Eastlands in the penultimate game of last season, and Dawson thinks the club's clash on the same ground could prove decisive.
'We have some big games coming up,' he said. 'We go to City and it may come down to that like it did last year but Liverpool are on a great run too. They're only three points behind us now.'
Spurs are set to discover the extent of Benoit Assou-Ekotto's injury. The influential left-back was forced off after suffering a hamstring injury in the build-up to Peter Odemwingie's opener and will be assessed by the club's medical staff when he returns to training on Wednesday.
Redknapp is already without defender Alan Hutton, while his replacement Vedran Corluka missed last weekend's game with a foot injury.
Ledley King hopes to make his first appearance since October on Saturday after returning to light training last week following a long layoff with a groin problem.
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Explore more:People: Michael Dawson, Alan Hutton, Simon Cox, Roberto Mancini, Ledley King Places: Liverpool, Europe