The Bantams, who charged to promotion via the League Two play-offs last season, chalked up their first win of the campaign last week with a 4-0 demolition of Carlisle in front of almost 14,000 at Valley Parade.
Yeates opened the scoring against the Cumbrians with a 25-yard effort which won Sky Sports' Goal of the Day.
Yeates told Sky Sports News Radio: "It was a nice way to get my first goal, but the main thing was to get the first win of the season. I thought we were good for the full 90 minutes and the gaffer has been pleased with us this week.
"It's a long time since I played at Valley Parade, but coming back here I didn't actually realise the size of the club and the support it has and it has taken me back a bit.
"The boys are a top bunch of lads and getting that first win has settled everyone down. There are a few lads who haven't played up a level who were anxious but getting that win has done them the world of good.
"I think that this squad, and if we get one or two new boys in, will have a right go this season and we could surprise a few people.
"I do think the two boys up front - Nahki Wells and James Hanson - will surprise a few centre-backs this season and if we keep them both fit we can pick up some good results."
Yeates, 28, also revealed that playing again under Phil Parkinson was a major factor in making the move north from Watford.
"Over the summer I spoke to the people at Watford and I got on great with the gaffer there (Gianfranco Zola), but I just thought I wasn't going to play and I didn't get offered a new deal.
"I spoke to a few clubs over the summer, but I had a chat with Phil (Parkinson) and having played for him before it just seemed right.
"Having a manager that can get the best out of you and one that knows you inside out is vital and probably the thing I need now at the stage of my career. I need to be playing regularly and hopefully playing for someone I know will work out well."
To hear the full interview with Yeates, plus more from former Barnsley manager John Hendrie, Millwall's Shaun Derry, Huddersfield's Adam Clayton and much more, download the latest Football League Hour.
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