The first team coach wants his top-six to be more ruthless after a generally inconsistent start to the season.
And he believes it will take much-needed pressure off the bowlers, who he says are spending too much time in the field and not getting enough chance to rest up properly.
“The top-six need to do the job because it’s been tough work for the bowlers,” said Gillespie.
“When we’ve looked back on the games, we’ve found that our bowlers were actually in the field bowling every day.
“That would suggest that maybe we haven’t quite nailed it with the bat yet.
“You need to give your bowlers a break, so that they can come out strong in the second innings and knock the opposition over, and the batters need to take responsibility.”
Gillespie’s comments come with Yorkshire third in the table – 11 points behind Durham with a game in hand – and boasting the only unbeaten record in the First Division after three wins and three draws.
That would suggest there is not a great deal wrong, and yet Gillespie believes his side can be even better and is challenging them to improve if they are to successfully defend their Championship crown.
The former Australia fast bowler believes those improvements can be made in all areas – including with the ball – but is particularly keen to get more from the batsmen.
So far, only Jonny Bairstow (80.4) and Jack Leaning (68.3) of the regular top-six are averaging more than 40, with others struggling for consistency and often grateful to the lower-order for bailing the team out of trouble.
A glance at the scorecards highlights the problem.
In the six Championship matches to date, Yorkshire’s sixth wicket in their first innings has fallen at the following totals: 186, 353, 222, 274, 225 and 96.
When added together, that equates to less than two-thirds of the total runs that Yorkshire have managed in those innings combined.
In mitigation, Yorkshire have not fielded the same top-six for two games running, primarily due to England call-ups at the start of the season and then, more recently, because England players have returned to the line-up.
But although everyone has contributed at some point, only Leaning (547 runs) and Bairstow (402), along with lower middle-order players such as Tim Bresnan, have hit the sort of standards of which they are known to be capable.
“We’ve spoken about the situation,” added Gillespie, whose side return to Championship duty against Nottinghamshire at Headingley on June 22.
“You can’t keep having lads down at seven, eight, nine doing a heap of the scoring.
“For me, batters seven, eight, nine – that’s plus tax. That’s VAT. That’s a bit extra.
“You need your top-six to be getting the job done.
“For us to be even better, which is what we need to be and what we keep challenging the lads to be every day – whether that be in training or in the matches themselves – it’s important that our top-six do the bulk of the scoring for us.
“Hopefully, we can improve on that as the season goes on.”
Yorkshire’s problems in the area were illustrated in their last Championship outing against Middlesex.
After dismissing their opponents for 212, Yorkshire were 96-6 before a brilliant hundred from Bairstow helped them to a final total of 229, which ultimately inspired a four-wicket win.
Bairstow’s impressive 125 not out stood out like a belch in polite company.
The next-highest score in the innings was 20, and Gillespie remains in awe of Bairstow’s performance.
“Jonny’s knock was one of the best knocks you’ll see,” he said. “It was one of the best knocks you’ll see in county cricket.
“I thought the way he batted with the lower order was simply outstanding, and in the context of that game and the situation we found ourselves in, for us to have a first innings lead going into the second innings was simply fantastic.
“I thought Jonny’s hundred against Hampshire in the previous home Championship match was a wonderful counter-attacking innings.
“This was another outstanding effort, and he’s a fantastic player who’s in special form.”
Gillespie knows Yorkshire cannot rely on one or two exceptional innings, however, and that they must raise the bar a tad higher.
He is confident they will do just that.
“We do feel we can be better,” he said.
“We’ve talked about the batting, but there’s definitely areas we can sharpen up on.
“We need to continue to work hard on our fielding, we need bowlers to maintain their focus and be really ruthless with their lines and lengths, and we need to keep pushing ourselves.
“We’re in a nice position in the table, but we’ve got to maintain our focus.”