Yorkshire reached the semi-finals of the 50-over tournament last year before losing to eventual champions Gloucestershire.
Yorkshire are the only side in the country without a win in the 20-over competition this season after three defeats left them bottom of the North Group.
But first-team coach Gillespie is optimistic ahead of his side’s Royal London opener against Worcestershire at Headingley today (2pm start).
“I’m really confident we can have a good campaign if we stick to the basics and hammer them home,” he said.
“We played some good cricket last year in the Royal London and had a number of good individual performances.
“The bowling attack did well and complemented each other, we ticked off some big partnerships with the bat, and we also fielded well.
“That’s going to be our biggest challenge – to try to improve those standards and make sure we’re ticking those areas off.”
Yorkshire have traditionally played better in the longer format of one-day cricket, with the 50-over game perhaps more closely resembling the skills required for success in the County Championship.
Gillespie’s men are joint-top of the Championship despite not having played to their peak, a source of frustration on the one hand but an encouraging sign on the other as they pursue a hat-trick of titles.
Yorkshire are clearly up against it in the T20 Blast, although by no means out of that competition seeing as it consists of 14 group games.
But if the club are to achieve any success in limited-overs cricket, Gillespie believes it is imperative that the players take individual responsibility.
The Australian made clear: “We’ve spoken a lot about the lads knowing their roles (in one-day cricket).
“We’ve had team meetings in the last couple of years and, as a coaching staff, have specifically said to the players, ‘Are you clear in your roles?’
“Sometimes they’ve said, ‘Yes’, and then, in a review, they’ve said that they didn’t know what their role was. But hang on a minute...
“So our big catch-cry (to the players) this year from the coaching staff is that you need to take personal responsibility for your performances and that there’s no excuses.
“If you’re unsure, if you’re unclear on anything, it’s your responsibility to make sure you are clear, and, if you’re not clear, to seek clarification. There can’t be any excuses and we’re not going to tolerate any.
“Lads have to take ownership of their games and take responsibility for their performances; we’re pretty hot on that.”
Gillespie’s belief that players must be 100 per cent clear on their roles within the overall team framework was strengthened during his coaching stint with Adelaide Strikers during the winter.
After leading the T20 franchise to the Big Bash semi-finals, the former fast bowler spoke of how the best players know their roles and how they are “adaptable cricketers as opposed to adapted cricketers”, meaning that they still retain the capacity to think on their feet and react accordingly.
As well as not tolerating excuses from his players, Gillespie does not put any forward himself when it comes to Yorkshire’s one-day displays.
The most obvious excuse would be that Yorkshire do not necessarily field their best side in limited-overs cricket, resting key bowlers such as Ryan Sidebottom and Jack Brooks, for example, to keep them fresh for Championship action.
But Gillespie stressed: “The bottom line is that we try to win each and every game that we play.
“Some people question us when we pick sides and we’re resting players, or whatever, but we genuinely strive to win every game.
“But, as I’ve always said when it comes to resting bowlers, if a guy has just bowled 50 or 60 overs in a week and then you’ve got a one-day game the next day, is he still one of your best four bowlers, taking into account the workload he’s had, his tiredness, the lack of preparation in terms of a different form of the game, and so on?
“That’s why we’ve always said that you need a squad of bowlers to get the job done. You can’t just rely on 11 players to play in all forms. You’ve got to have a squad mentality.”
Yorkshire squad (v Worcestershire): Ballance, Bresnan, Carver, Coad, Hodd, Leaning, Lees (capt), Lyth, Patterson, Plunkett, Rashid, Rhodes, Willey.