Son was dismissed just before the break for pushing Jefferson Lerma to the ground, while half-time replacement Foyth received a red card only two minutes and 13 seconds after the restart for an ugly lunge on Jack Simpson.
The Cherries' numerical superiority finally told in stoppage time when Nathan Ake headed home from a corner.
Asked whether he thought Son's dismissal was harsh, Pochettino told Sky Sports: "There is nothing to say. I respect the decision of the referee and my opinion is not too important. You cannot change what happened before now."
On Foyth's red card, Pochettino added: "Again, I didn't see but I have to respect the decision of the referee.
"It's unlucky for us – first of all with Sonny, then with Juan. We tried to play with one less. It's unlucky for us. There is nothing to say.
2:13 - Juan Foyth has been sent off just 2 minutes and 13 seconds after being substituted on, the quickest a substitute has been sent off in a Premier League game since Steven Gerrard vs Man Utd in March 2015 (38 seconds). Skedaddle. #BOUTOT pic.twitter.com/TcOZ3PtznD— OptaJoe (@OptaJoe) May 4, 2019
"I think the effort was massive. With nine players, we defended well and played a very good game, but not enough because in the last minute we conceded."
Spurs may now need to take something from their game against Everton on the final day of the season to secure a top-four finish, while they travel to Amsterdam on Wednesday looking to overturn a one-goal deficit from the first leg of their Champions League semi-final in London last week.
Despite the uncertainty surrounding their finish to the season, Pochettino is delighted with what his side have achieved.
"We are third, are competing for the top four and we are in the semi-finals of the Champions League," he said.
"If you look back at our first game of the season in the Premier League, everybody is trying to be in the position that we are in today. I am proud about the season."