Jose Mourinho's men capped off a fine week that saw them beat Paris Saint-Germain to reach the UEFA Champions League semi-finals by overcoming Swansea City 1-0 on Sunday to keep pace at the top of the table.
Leaders Liverpool head Chelsea by two points following a 3-2 victory over third-placed Manchester City, who are a further five points back with two games in hand.
Chelsea visit Liverpool in two weeks' time in a game that could well decide the destination of the trophy, and Cech feels Chelsea's knowledge of big games may give the London club the edge.
"Nobody expected anything from Liverpool this season and they're in contention - it’s why they've been able to play without pressure so far," Cech told the London Evening Standard.
"But let's see how they will cope when it comes to the last hurdle. They will have to jump over it. They have been doing remarkably well but we're still around.
"Obviously, we have to wait for one slip up from Manchester City but if we win our games we have a chance.
"We have players who are used to playing big games. Sometimes when you have a young team full of enthusiasm they don't feel any pressure, they just play.
"But we have just four games to play now and if we win all of our matches, we will be there right to the end. That's what we will try to do, to go game-by-game, try to win them all and then we'll see where we'll be. We will go for it."
Chelsea's fixture list is made busier by their upcoming Champions League last-four tie with Atletico Madrid, a challenge Cech is relishing.
"We're also in huge matches in the Champions League so there is a bit of congestion but that's just the way it is," he added.
"It is always great to be a position like this, where you play for everything because it is so exciting.
"It's going to be very tough to play three games like this in a row but we are a top club and as a player at a top club you come here for this opportunity to play huge games."
