Chelsea moved four points clear of United at the summit thanks to a 1-0 victory over Bolton. Nicolas Anelka's first-half strike, his first in 14 games, settled the outcome and kept Chelsea on course for an historic League and FA Cup double.
"They know they're under pressure," said Cech. "At the weekend there is the Manchester derby and we play a London derby at Tottenham. It can be a decisive week."
He added: "It can change the position in the Premier League a lot if we manage to win our game and the others lose theirs. It could also go the other way and change everything for the last three games.
"But beating Bolton was a massive step forward. We can play good football and score goals but when a game isn't going our way and we have to fight and dig deep, we can do that. We showed it against Bolton.
"I have been at Chelsea for six years and just kept my first clean sheet at home against Bolton so now it's time for our record at White Hart Lane to change too.
"Last season everything went wrong. There was a bomb alert, the game was delayed, we were kept waiting and then we started slow and lost 1-0. Even though we had chances, it was not our day. This time it's going to be different for us."
Meanwhile captain John Terry admitted Chelsea were affected by a touch of the jitters against Wanderers. The visitors had chances to snatch a draw and boss Owen Coyle was furious that referee Lee Probert rejected two penalty appeals."
"We were probably a bit slow in the tempo of our play and were taking too many touches," admitted Terry. "Nerves with us not winning the Premier League for three years took their toll late on but we managed to hold on.
"We are getting closer week by week but it is just important that we keep winning. Man United, Arsenal and us have all got tough away games this weekend. We are just concentrating on ourselves and we have a little cushion now."