However, the hosts equalised early in the second half when Calum Chambers put the ball into his own net in the 56th minute.
Spurs' Harry Kane had a goal disallowed for offside and saw his acrobatic effort headed off the line in the second half as Flamini scored his second of the night for Arsenal when he volleyed home the winner in the 75th minute.
"We deserved more. We created more chances, dominated the second half and you know you need to kill the game," Pochettino, who suffered his first North London derby defeat, told the club's website (www.tottenhamhotspur.com).
"The way we played was good, but the result is most important, so we're all disappointed."
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The Argentine is keen to move ahead from the loss and focus on their next Premier League game on Saturday against table-toppers Manchester City, who beat Sunderland in the League Cup.
"We need to prepare for City... we have to be strong," Pochettino said.
Arsenal manager Arsene Wenger heaped praise on holding midfielder Flamini, who was heavily linked with a move away from the club during the summer transfer window.
"He is a fighter and he is a winner as well. I told him at the start of the season it might be difficult for him to be a starter but he decided to stay and he did fight," Wenger told reporters of the 31-year-old.
"I fought to keep him but he is at an age where you always consider what is important at that age, which is to be focused and stay in the team.
"If they do not manage to do that it is better you let them go, but he wanted to stay."
Flamini, who is currently in his second spell with the Gunners, said he had to prove a point after making his first start since playing in a pre-season friendly in July.
"I had a point to prove because I hadn't played for a while but I'd been working hard and it was my game (against Tottenham), but my team-mates did a great job too," said Flamini, who made 33 appearances last season.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
