Tuesday night Manchester United at Old Trafford. Before February is out, Valencia home and away in the Europa League knockout stages. But Tony Pulis does not consider he has bigger fish to fry: Stoke City arrived at Pride Park at full strength and with minds fixed on another tilt at the trophy they came so close to last year.

"The thing that we want to do – and the [Coates] family are 100% behind it – is to have a go in the cup games," Pulis said. It is a strange world in which a club's attempts to stay in competitions should need explaining, but such is football these days. A team sheet showing three forwards (Jonathan Walters played on the right of midfield) and a strong Stoke back line raised eyebrows before kick-off. "I wanted to show Derby the respect they deserve. They've had a fantastic run and we knew it was going to be a tough game."

In the end, it was not nearly as difficult as Pulis imagined. Five minutes in, no one in a Derby shirt could react quickly enough as Glenn Whelan's centre was heel-flicked towards the near post by Marc Wilson, and a touch from Robert Huth enabled Cameron Jerome to give Stoke the lead from close range. Replays showed the striker was offside as Huth played the ball on in a crowded penalty area, leaving the Derby County manager, Nigel Clough, to bemoan his luck.

For him, this tie was an opportunity to test his team – unbeaten since Christmas and climbing towards the Championship's play-off places – against a Premier League side; the goal altered the contest and the opposition. Still, there were signs that Derby could prosper against less stubborn opponents, of which the top flight holds several. Craig Bryson and Jamie Ward were pests in the first half, testing the agility of Huth and Ryan Shawcross and working openings for Paul Green and Jeff Hendrick.

"We played some good stuff and got them on the back foot a little bit," said Clough, who was without Theo Robinson and Ryan Noble up front and had Nathan Tyson able only to come on from the bench. "It's a great learning curve for Callum Ball and Jeff Hendrick, at 19 years old, playing against the eighth-best team in the country and battling away with two big centre‑halves."

The second half gave Derby's forwards fewer learning opportunities, and provided a sterner test for their team-mates further back. The goalkeeper Frank Fielding did well to palm the ball away after Matthew Etherington had nutmegged Jason Shackell cutting in from the right, and the travelling supporters behind him were already rising to their feet when he managed to get two hands to Jermaine Pennant's 40-yard free-kick.

Stoke were enlivened by Pennant's arrival, and by the time Pulis added Kenwyne Jones and Ricardo Fuller, Derby had retreated. Seven outfield players looked to protect Fielding's goal as Pennant tossed in a corner in the 81st minute, but Huth – who had earlier been denied by the post – beat Green to the ball just in front of the penalty spot and struck it under Fielding.

The goal ensured that Stoke would play in the fifth round in the same week as the Valencia double-header. "February is a big month for us," said Pulis, suggesting he would make one or two changes to the team to face a "revved-up" United, put out of the Cup by Liverpool earlier in the day. "We've got some fantastic games coming up and if we can get a home draw then we'll be absolutely delighted."