United finished ninth as they returned to the Scottish Premiership following a four-year absence and manager Micky Mellon often stressed his team were developing as top-flight players.
There is a new man in charge in the shape of former academy coach Tam Courts and the only new player to make the first team so far is Charlie Mulgrew, while Marc McNulty has moved on.
But Reynolds feels expectation levels will rise among the United support ahead of Sunday's league opener at Aberdeen.
"There's always pressure there but the pressure increases," the former Motherwell and Dons player said.
"I think you get allowances made as the new boys coming in, that you are getting used to life in the Premiership.
"A lot was made last season of boys who hadn't played there before, it was a new level for them.
"We now have a year's experience of that. We have had a chance to see what it's all about, a chance to get to grips with it, and we are the better for it.
"So there's loads of pressure on us. We put a lot of pressure on ourselves internally as a club. We want to go and do well, and we need to start that on Sunday."