Arsenal suffered a 2-0 loss to their north London rivals at White Hart Lane, second-half goals from Dele Alli and Harry Kane proving decisive.
The result leaves the Gunners six points adrift of the top four and a massive 17 behind second-placed Spurs, with Cech hugely frustrated after his fine individual display – one that saw him make nine saves – went unrewarded.
"I feel angry and disappointed because obviously this is not a game we wanted to lose," Cech told reporters after the match.
"This is a very big disappointment for us. With all the emotions, I have to say that we met a team that was full of confidence, well organised and they are having their best season. I think that showed, that little bit of more confidence and quality on their side.
"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 and obviously we are very disappointed because it is 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.
"The goals obviously made a big difference. At half-time I felt we were in the game and in the second half we wanted to improve, we wanted to play to win the game.
"The second half was our best half - they put us under pressure, created chances and in the end they scored two goals."
Arsenal still have a game in hand on their closest Champions League rivals and were boosted when Manchester City and Manchester United were both held to draws by relegation candidates Middlesbrough and Swansea City respectively.
"We need to win our remaining games and then we will see," added Cech.
"The others are losing points as well sometimes so our job is to win the remaining games and then we will see.
"We need to win the remaining games and hope some of the teams ahead of us slip.
"Our target is to play for titles so we are disappointed with our season because we aren't playing for a title.
"We have five games to play and we are out of the title race. It was not the objective so we are disappointed with that."