The Everton defender predicts their Group H rivals will provide a stern match for Roy Hodgson's side following their comparatively simple victory against minnows San Marino
The Everton centre-back was rarely troubled on Friday evening as England collected their first home win of the World Cup 2014 qualifying campaign.
Jagielka was pleased to record a morale-boosting victory but acknowledged that the Euro 2012 co-hosts would present a far sterner proposition away from Wembley.
"Three points in the bag, five goals scored and none conceded, as far as we're concerned it was a good professional job done," Jagielka told the Football Association's official website.
|8/1||Phil Jagielka is 8/1 with William Hill to score at anytime against Poland
"It was all about a clean sheet from the defensive point of view and for the front men to create and score goals and get some confidence heading into Tuesday.
"We're expecting a much more difficult game on Tuesday night."
England will have to do without Chelsea duo Frank Lampard and Ryan Bertrand at the National Stadium in Warsaw, while Theo Walcott will also sit out the match after suffering a bruised lung in a challenge with San Marino goalkeeper Aldo Simoncini.
But Jagielka insists Roy Hodgson's side have more than enough strength in depth to deal with the latest injury setbacks.
"Frank's done well for England, especially recently, so we will be missing him," Jagielka commented.
"But if you look at the other night's game, Michael [Carrick] and Tom [Cleverley] did fantastically well and we've also got our captain [Steven Gerrard] to come back, so cover for Frank not being here is looking really good at the moment."