Three points against Liverpool at Anfield on Sunday would have put the reigning European Champions back up to third ahead of Arsenal and Tottenham in the tense battle for a top-four finish.
But Luis Suarez's late leveller means only two points separate the three London rivals as the season draws to a dramatic conclusion.
"We are in a position where we fight for everything," Cech told the London Evening Standard.
"We have a lot of pressure playing in the Europa League because we obviously want to win it. Every league game we are in the fight for the top four places and it's very tight there."
The Blues shot-stopper was unhappy with the amount of added time given at Anfield, allowing the controversial Suarez to grab a last-gasp winner after he had earlier avoided punishment for biting Branislav Ivanovic.
"We had a disappointing end to this game," Cech added.
"It's unusual to have six minutes. I have been a Chelsea player since 2004 and I have never had six minutes in my favour when I was losing."