Cech expects Euro battle to go to the wire
That left the Blues in fourth place on 62 points, a point behind third-placed Arsenal. Spurs are fifth, also on 62, after a draw at Wigan on Saturday.
Chelsea's midweek victory in Basel in the first leg of the Europa League semi-finals will have boosted confidence in Rafael Benitez's squad.
But Cech believes the pressure will continue to mount until the very end of the campaign and Chelsea cannot afford any slip-ups against a Swansea side that beat them in the last four of the League cup earlier this season.
"The top-four fight is undecided and won't be until the last game. For the neutral it will be exciting until the last day," Cech said.
"We have a big game in every match we play. This is the way it goes and we can't forget about Swansea. We have to take things step by step."
Looming is the home showdown with Tottenham on May 8 but David Luiz, the scorer of the last minute winning goal in Basel, warned it is too soon to target that clash as a potential decider in the race for the top four.
"We need to take three points in all the games. Spurs is one key game for us, but we need to play well in the other games too," Luiz said.
"We need to keep focused for the future, particularly on Sunday against Swansea, because they have a very good team.
"You saw that in the semi-final of the League Cup. Of course we believe we will finish the season strongly.
"We have an opportunity for that. I want that and my team-mates want that as well."
Having lifted the League Cup - the club's first major honour - Swansea's remaining target is to secure a top-half finish and Wales centre back Ashley Williams claims Michael Laudrup's side have reason to believe they can inflict another blow on Chelsea.
"We can get a result there. It will be tough, that's obvious, but we've been there and nicked a win before," he said.
Williams's form this season has seen him linked with a move away from the Liberty Stadium, with Liverpool and Arsenal both touted as possible destinations.
But the 28-year-old said: "If you're being linked with other teams it means you're doing your job properly.
"I can't think about things like speculation, I'm here with Swansea, enjoying playing in the Premier League and being captain and that's what I'm focused on.
"The only time I think about it is when people stop me in the street or journalists ask me about it.
"There's no point in me thinking about it otherwise because I have too much else to focus on in my own personal life and on the pitch and the training ground for Swansea."
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