The club have failed to win any of their first six games in the NatWest T20 Blast and the Royal London Cup.
Yorkshire lost their first three T20 matches before suffering a total washout against Birmingham Bears at Edgbaston on Friday.
And they are still seeking their first win in the 50-over tournament after just one over was possible yesterday at Chesterfield, where the game against Derbyshire was rained off to deny Yorkshire the chance to hit back from their defeat to Worcestershire last Tuesday.
For the record, Tim Bresnan bowled a maiden to Derbyshire’s Ben Slater at the Queen’s Park venue, which was then hit by torrential downpours before play was abandoned at 12.45pm.
Yorkshire, who won the toss, had a strong side out, with New Zealand batsman Kane Williamson making his first appearance of the season, and conditions looked perfect for the Yorkshire bowlers.
But Gillespie was phlegmatic about the latest setback, and the first-team coach is confident his side can find their best form.
“It’s obviously frustrating to have another game rained off, and we had the opportunity to bowl first and to impact early,” he said.
“We wanted to get back on the horse, so to speak, and to play another game, and it would have been nice to have got a positive result.
“At the same time, the lads are in a fantastic place at the moment and there’s a lot of optimism about our shorter-form cricket.
“I know things haven’t quite gone to plan so far, but I’m really confident we’re going to turn it around.
“We’ve got a really good squad, and we feel that we’re going to have a real impact this summer.
“There’s a long way to go. People talk about our T20 form, but last year Lancashire won the competition and lost six games in the group stage.
“It’s not all doom and gloom from our point of view.”
Gillespie said that Yorkshire had an honest chat after their 50-over defeat to Worcestershire, who won by seven wickets at Headingley with 24.3 overs to spare.
It was a poor performance, but Gillespie insisted that he came away feeling buoyed by the players’ attitude.
“We had a really good chat after that match,” he said.
“It was one of the best post-match chats I’ve been involved with, and it was just very honest, open and constructive. There was no finger-pointing or raising of voices; it was just a good, honest, critique of the performance.
“That’s what you want, and that’s how the lads will learn and improve.
“In a funny kind of way, I came away from that game feeling really proud of the players. While it was disappointing to lose, I was really proud of how the lads spoke in the dressing room and how honest they were. “As a coach, that makes you proud, and to see how much the lads were hurting.
“I know some people might be worried that results haven’t gone our way so far in one-day cricket, but we’re feeling tight and feeling strong.”
Yorkshire return to 50-over action tomorrow when they face Northants at Scarborough (11am start).
They expect to have Adil Rashid available after the leg-spinner was left out yesterday as a precaution due to a stiff neck.
Yorkshire are also casting an eye over another spinner in the familiar form of Azeem Rafiq.
The 25-year-old off-spinner, who last played for the club in 2014, is turning out for the second team as he looks to rebuild a promising career.
“Azeem is with us and we’re having a look at him,” said Gillespie. “I’m a massive fan of his, and although he fell a bit by the wayside and his performances dropped off, I think he had a lot of stuff to sort out in his personal life as well.
“Since then, he’s gone away and got himself married, and I think a bit of time away from cricket has probably done him the world of good. We’ll assess him, and we’re not looking any further ahead than that at the moment.
“He’s a bit underdone because he hasn’t done the professional cricketer thing for a little bit now.
“It’s just about him getting back and playing some cricket and enjoying himself really.
“But, in my opinion, he’s a very good young bowler. He’s got a brilliant cricket brain, and he’s a great kid too.”
Gillespie played down suggestions that the club may look to the loan market to help them through a personnel crisis.
The club could be without six bowlers for their next Championship match against Durham next Monday, with Ryan Sidebottom, Jack Brooks and Matthew Fisher injured, and David Willey, Adil Rashid and Liam Plunkett potentially involved in the one-day series against Sri Lanka.
“I don’t think that (the loan market) is something we’d look at,” said Gillespie. “We’ve got a lot of bowlers, with the likes of James Wainman, Ben Coad, Will Rhodes and Jared Warner among the potential options.”