There was a lot of expectation surrounding the Potters this summer following the signings of Michael Owen and Charlie Adam, but they are just four points off the Barclays Premier League relegation zone after 12 games.
Key to Stoke's failure to put more daylight between themselves and the drop zone has been the club's dismal away form. Monday's 1-1 draw at West Ham was the 16th successive game Stoke have failed to win on their travels.
And with a difficult festive schedule ahead, Crouch knows maximum points in Stoke's next two games - at home to Fulham and Newcastle - are vital.
"A point at West Ham is deserved but with two home matches we have to start pushing up the league now," said Stoke's top scorer.
"We have got to look at our home matches now. Our home form has been keen to our success. I'm sure we will continue with that.
"We should be looking at a top-10 finish. There's no reason why we can't achieve that and hopefully a good cup run. That's what we should be aiming for."
Newly-promoted West Ham, meanwhile, continue to defy the odds and sit in joint sixth with a third of the season gone.
Tough matches against Spurs, Manchester United, Chelsea and Liverpool lie ahead for the Hammers, but defender Joey O'Brien, who scored the equaliser Monday, thinks the team have little to complain about.
"Next week is a tough week but it's what the Premier League is about," the right-back said.
"We were in the Championship last year and when times got bad that's what we said our aim was - to play against the likes of Tottenham and Manchester United - so we look forward to it and we will try to get a result at White Hart Lane."
With Tottenham having lost three successive games, O'Brien thinks the Hammers are in a good position to beat their London rivals away for the first time in 13 years this Sunday.
"We think we're a good team. That's how we go out and play," the Republic of Ireland defender said.
"We don't have a mentality of a newly-promoted team where other teams can just roll you over. We have some quality players that have played in the Premier League for a long time.
"We're not going there just to get beat and turn up and enjoy it. We're going there to get results. We have nothing to lose against these teams."
Hammers manager Sam Allardyce echoed O'Brien's comments, telling talkSPORT: "We have to say we are a little more consistent (than Tottenham) if we have more points than them.
"Every game is a tough game for us but I thought we did extremely well against Stoke based on the injuries we had.
"We have played 12 matches and we are (joint) sixth in the table with 19 points.
"Sixth in the table is a pretty good start for anyone, let alone a team that has just been promoted."
Despite being 26, O'Brien's strike - a close-range finish from Gary O'Neil's cross - was his first in top-flight football.
"I've always said if you can get yourself into the box it doesn't matter who you are or what position you play in - if you buy the ticket you might get the goal and Joey bought the ticket and got the goal for us," Allardyce said.