Nani opened the scoring for United in the 27th minute when he burst into the area and clipped the ball in at the near post before Crouch headed home to equalise seven minutes after the break.
The draw means Stoke take their first point from United while the Barclays Premier League leaders dropped their first points of the season.
Striker Crouch believes the strong team spirit at the club will lead them to success this season.
"It's always nice to get your first goal for your new club In front of your home supporters," he told ESPN.
"Against Manchester United it's really pleasing for me.
"We worked so hard and I've never know a team spirit like it. The team spirit here and the willingness to work, that's why we got a result today.
"We created a few chances and as long as we play like that we'll do well this season.
"Since I've been here I've never known a character and willingness to work like Stoke City.
"The manager's instilled it and when I first signed he said 'you've got to be part of that and work hard' and that's what he expects and that's why we've got the result here against Manchester United.
"They're in top, top form and that win was down to hard work and that little bit of quality and that's why we get those results."
Stoke defender Ryan Shawcross praised man-of-the-match Crouch for his second-half equaliser.
"Our overall performance was fantastic and the big man's popped up with a goal and we brought him here to do that.
"He's a great player."
But he refused to accept the absence of prolific United striker Wayne Rooney meant the Potters had an easier time against the league leaders.
"Obviously he's in great form but they've still got some great players out there and it's a great point for us." Shawcross added.
Source: Team Talk
Source: Team Talk