0222 GMT July 20, 2019
Goals from Dele Alli and Harry Kane saw Spurs, second in the Premier League, move a huge 17 points clear of Arsenal and ensure it would finish above its local rivals in the table for the first time since 1995, supersport.com reported.
Tottenham is still very much in the title race, with Mauricio Pochettino's team just four points behind leader Chelsea, with both the top two having four league games left this season.
By contrast, Arsenal is sixth and six points adrift of fourth-placed Manchester City, who occupies the last Champions League place on offer to English clubs, although the Gunners does have a game in hand.
Arsenal's next match is at home to Manchester United, who are fifth and are five points ahead of Arsene Wenger's side, this weekend.
"I feel angry and disappointed because obviously this is not a game we wanted to lose and this is a very big disappointment for us," Cech told Arsenal's website.
"It hurts because it was a huge game for both teams. They needed to win to keep their title chances alive. We needed to win to keep our Champions League finishing position [hopes] alive.
"Obviously we are very disappointed because it's a north London derby, it means a lot to the fans and it meant a lot to the club, to us. We needed three points and in the end we have none."
As for finishing below Tottenham, Cech said that was the least of Arsenal's concerns.
"Our target is to play for titles, so we are disappointed with our season because we aren't playing for a (league) title," he explained.
"We have five games to play and we are out of the title race. It was not the objective (to finish below Tottenham), so we are disappointed with that," the former Chelsea star added.
"But Tottenham finishing above us or doing better is one thing, but I think the most important thing for the club, for the players, for everybody is to reach your own targets, not to worry about what the others are doing."
Sunday's match was the last derby ever to be staged at White Hart Lane after Tottenham confirmed earlier last week they would play all their home games at Wembley next season while a new stadium, close to their home for more than a hundred years, was being built.
"It was a very good game from everyone, from start to finish," said Tottenham's Jan Vertonghen.
"It was the perfect day to put on a performance and I'm very proud of it. We knew we had to focus. It was the last north London derby at the Lane and that's so special for so many people."
"I know what it means. It was a very big day and we've one more to come. Let's hope we can make that one special too."