The Potters broke their own transfer record to bring in Crouch for a fee of around ?10million on deadline day, after he had fallen down the pecking order at Tottenham.
The striker has performed well for Stoke so far and scored goals in the 1-1 draw with Manchester United and 2-1 victory over Besiktas.
He concedes that he would have started to feel the strain if he had not opened his account for his new club by now, telling Sky Sports News: "You obviously want to get the first one out the way early, which I've done."
Stoke have had a couple of disappointing results this season, having lost at Sunderland and Swansea, but they are still eighth in the Premier League and have shown what tough opponents they can be against the likes of Chelsea, Liverpool and Manchester United.
Crouch is delighted with the signs of progress he has seen at the Britannia Stadium and hopes to play a major part in a bright future for the club.
"We've played Chelsea, Liverpool and Man United and got five points out of those games," he said.
"We've still got a lot of teams to play at the Britannia and, while to lose a couple away from home has been frustrating, I feel I have joined a really good club, a club on the up."
Source: Team Talk
Source: Team Talk