Spurs were beaten 1-0 due to Nathan Ake's stoppage time goal, but it was an action-packed game at Dean Court.
To make matters worse for Spurs, Juan Foyth lunged in recklessly with a risky challenge on Jack Simpson just three minutes into the second half, leaving Pawson with little choice but to brandish a second red card in remarkably quick succession, with the visitors now down to nine men.
They had their chances in the first half at the Vitality Stadium, but found debutant goalkeeper Mark Travers in inspired form. Ake's late victor also means Tottenham have lost six consecutive away Premier League matches for the first time since May 2004. "Ajax is a good team, but they were lucky to get to where they are".
"You need that spirit to win away from home, you need things to go your way, you need that extra quality".
"Anything still could happen".
Sarri warns Chelsea of Eintracht threat
The Blues go into tonight's game with only two recognised first-team centre-backs fit in David Luiz and Andreas Christensen . He started the 1-1 draw against Manchester United at Old Trafford on Sunday but limped off after 65 minutes.
Tottenham's Premier League top-four fate will go down to the final day after they suffered a late defeat at Bournemouth having had two men sent off.
With the win the Cherries moved up to 12th in the table on 45 points, while Spurs are now only four points ahead of Arsenal in fifth with one game to go, as the Gunners have a game in hand on them too. "I do think Tottenham will be one of those, but who knows".
Spurs head to Amsterdam trailing 1-0 from the first leg, and with injuries piling up and Tottenham winning just four of their last 15 games in all competitions, yet another fine season is threatening to end on a sour note.
The four-time European Cup winners eliminated defending champions Real Madrid and the Old Lady en route to their semi-final showdown against Tottenham Hotspur.
Eddie Howe told Sky Sports Bournemouth's summer business will be their biggest yet as they look to improve for next season. Their quarter-final meeting with Juve was more of a close affair, but the Amsterdammers answered everything asked of them, inflicting a consecutive last eight exit on Allegri's men now boasting five-time Ballon d'Or recipient Cristiano Ronaldo.