Spurs' pursuit of a top-four spot looked plain sailing a month ago as they led fifth-placed Chelsea by 10 points, but they have hit choppy waters in recent weeks.
Saturday's defeat to West Brom meant they have taken just four points from the last four games, while Chelsea have taken 12 following their win over Liverpool on Sunday to cut the gap to two.
Spurs remain in pole position, knowing they will finish above both Chelsea and Liverpool if they win their remaining two games of the season.
The first of those is against Newcastle at Wembley on Wednesday and Pochettino insists his side will give everything to get the job done.
"To play Champions League is the dream of everyone and for me it's impossible to think and not give your best when it depends on you to win," he said.
"It's massive because the Champions League is the best competition, with the Premier League, in the world.
"It's in our hands. We need to die to try to achieve that. It's not, 'We need to play like this, with two centre-backs or two strikers or two keepers'. It's about the players dying trying to achieve it.
"If we cannot, we cannot. That's different and we need to analyse why. Now it's to be altogether and fight with our fans and create a good atmosphere and try to achieve altogether to play Champions League football in the new stadium."