With Celtic still hurting from last Sunday's injury-time defeat at Ibrox, which extended Rangers' lead at the top of the Scottish Premier League into double figures, the Hoops travel to Falkirk on Sunday knowing anything less than a victory is unacceptable.
However, Celtic have dropped four points against bottom club Falkirk this season and Pressley has challenged his side to add a victory to their two draws.
The former Scotland defender knows all about the pressures of playing for the Old Firm, having been one of the few men to represent both sides.
But he has urged his own players to concentrate on their game plan and not fear Celtic's response.
"The pressure is very much on Celtic," Pressley said. "They are on the back of a disappointing result against Rangers and their supporters will demand the correct reaction.
"Everyone outside our own camp will be expecting a Celtic win but we're looking forward to the challenge.
"On two occasions this season we have played against them and taken points and we're looking to go one stage further.
"We'll work towards our game plan and hopefully we can put it into practice.
"Our sole concentration will be on our own preparation and how we go about the game. Our focus is on winning the game and not anything else."
Pressley was encouraged by some aspects of his team's performance last weekend, despite their 3-0 defeat by Dundee United.
And he has ample cause for optimism given his only home match in charge so far was when Falkirk recovered from the loss of an early goal to beat Aberdeen 3-1.
That was only Falkirk's second SPL win at home this season and Pressley is desperate to build on that record.
"That's been one aspect that has been disappointing this season, our home form," he said.
"We want to put that right and make the Falkirk Stadium somewhere where teams don't enjoy coming to play. We can only do that by winning games.
"We had a good positive result against Aberdeen and if we can follow that up with another positive result we can get some momentum."
Celtic 4/11, Draw 10/3, Falkirk 7/1
Source: Team Talk