London - Mauricio Pochettino insisted on Saturday that nine-man Tottenham won't let a "cruel" 1-0 defeat at Bournemouth ruin their bid to finish in the top four and reach the Champions League final, while Cardiff were relegated after their 3-2 defeat against Crystal Palace.
Tottenham's South Korea forward Son Heung-min was sent off for a needless push in the closing moments of the first half and Argentine defender Juan Foyth saw red for a studs-up lunge soon after the interval.
Pochettino's side looked like they would hold on for a point as the match entered stoppage-time, but Bournemouth defender Nathan Ake ended third-placed Tottenham's stubborn resistance to delay their attempt to guarantee a place in the top four.
A win at Dean Court would have achieved that aim, but fourth-placed Chelsea will now go above Spurs if they defeat Watford and Arsenal, currently fifth, will move to within one point of their north London rivals if they beat Brighton on Sunday.
"Of course it is difficult to get something positive. We made a massive effort," Pochettino said.
"We need to move on. We have ahead two finals. It is in our hands. If it does not happen we will be proud because nobody expected Tottenham to be in the position they are today."
Tottenham's ninth defeat in their last 15 games in all competitions means they need to wait for Sunday's results to see if they need to win their final Premier League game of the season at home to Everton on May 12.
It was the worst possible preparation for their bid to overturn a 1-0 deficit in the Champions League semi-final second leg at Ajax on Wednesday.
"We are fighting six teams. It's impossible for all six to get the top four, whatever happens I will feel proud and whatever happens in the semi-final I will be proud," Pochettino said.
Cardiff needed a win to have a realistic chance of beating the drop on the last day of the season, but they were out-classed by Palace in south Wales.
Wilfried Zaha put Palace ahead in the 28th minute before Martin Kelly's own goal three minutes later gave Cardiff hope.
Michy Batshuayi restored Palace's lead in the 40th minute and Andros Townsend made it three after 70 minutes, with Bobby Reid's 90th minute goal little consolation for Cardiff.
Third bottom Cardiff are four points behind fourth bottom Brighton with only one game remaining, ensuring they will join already relegated Huddersfield and Fulham in the second tier next season.
The Bluebirds will make an immediate return to the Championship after last season's promotion, their fate sealed by a dismal run of nine defeats in their last 11 league games.
It won't be a season fondly remembered by Cardiff, with their relegation coming after the tragic death of striker Emiliano Sala, who died in a plane crash en route to Wales before he had even played a game for the club.
"They've tried hard. We've shown limitations today and that's why we are where we are," said Cardiff boss Neil Warnock.
In their first season back in the top-flight, Wolves moved a step closer to sealing an impressive seventh place finish as Leander Dendoncker clinched a 1-0 win over relegated Fulham.
Belgian midfielder Dendoncker netted in the 75th minute at Molineux to give Wolves a third successive win.
Nuno Espirito Santo's team are four points clear of eighth placed Everton, who only have one game left, and six ahead of ninth placed Leicester, who have two matches remaining.
If Manchester City win the FA Cup final against Watford later on May 18, the team which finishes seventh will go into the Europa League qualifying rounds next season.
In the 88th minute, Fulham provided an historic footnote as Harvey Elliott was sent on to become the Premier League's youngest ever player at 16 years and 30 days.
English midfielder Elliott, born in April 2003, surpassed the previous record set by former Fulham player Matthew Briggs, aged just 16 years and 65 days in 2007.
Marko Arnautovic ended his 11-game goal drought with a brace in West Ham's 3-0 win against Southampton at the London Stadium.