The Yorkshire first-team coach conceded his side have yet to hit top gear in this year’s County Championship.
Yorkshire were denied a seventh successive Championship win yesterday when their game against Sussex at Hove ended as a draw.
Rain washed out the final day after Yorkshire scored 494 in their first innings, Sussex replying with 493-7.
It was not Yorkshire’s best display of the season, but the pitch was flat and Sussex fought hard in their battle to avoid the drop.
The stalemate stretched Yorkshire’s unbeaten record this summer to 12 games (eight victories and four draws) and edged them ever closer to the trophy.
Yorkshire have four games left, against Somerset (H), Middlesex (A), Hampshire (A) and Sussex (H), and appear likely to clinch the title in the second of those fixtures at Lord’s.
Gillespie’s team are 30 points clear of Middlesex with a game in hand, but the Australian admitted Yorkshire have yet to hit the heights to which they aspire.
“We talk about it – the perfect game,” he said.
“What does it look like?
“We challenge the lads. Paint us a picture. What does the perfect game look like?
“It’s rare to have a perfect game, but there’s nothing wrong with aspiring to it.
“We haven’t yet had it this season, so we need to keep striving.
“We’re continually looking for ways to be better.”
Yorkshire’s quest for perfection is bad news for the rest of Division One, whose imperfections are such that Gillespie’s side are still far and away the best in the country.
The title is now so close that the only question is when it will be mathematically confirmed, although Gillespie is continuing to insist that he is “not even thinking about it (the title)”.
For Gillespie, it is “all about the processes involved on a day-to-day basis as opposed to the end result”.
And he insists there is still room for improvement.
“I want us to be better each and every day, whether that’s in a game or in training,” he stressed.
“We have to strive for that perfect performance.
“I remember we had a good win up at Durham, for example, but that was far from a perfect performance.
“We were 190-odd for six and then two lads (Bairstow and Bresnan) went out and smote it.
“That got us to a big total and then we bowled Durham out twice.
“So although it was a great win, it wasn’t a perfect performance by any stretch of the imagination.”
Gillespie was reasonably satisfied with his side’s work at Hove, although it did contain familiar inconsistencies.
Yorkshire were in early difficulty at 22-2 on the opening day and then 134-4 before a seventh-wicket stand of 197 between Gary Ballance and Tim Bresnan helped them reach an imposing total.
“It wasn’t our best display,” said Gillespie.
“We’ve found ourselves 20-2, 30-3 on a number of occasions this year, and that’s something we certainly need to address.
“A perfect performance might start with a century-plus stand from the opening batsmen, and we’ve talked often about our top-six needing to take more responsibility.
“We don’t want to be leaving it to numbers seven, eight and nine.
“But the pleasing thing is that we always seem to have found a way. What we haven’t done is panic, and we saw that once again against Sussex this week.
“Gary and Tim played really well to get us up to a decent score.
“It seems that someone is always putting up their hand.”
The County Ground pitch stifled the Yorkshire attack, particularly after Sussex employed the heavy roller.
It did not help the visitors, who have so much depth that they were able to leave out leading wicket-taker Jack Brooks.
“I was very pleased with our bowling until tea on the third day, and then Sussex scored 210 in the last session,” said Gillespie.
“Fair play to them; they were looking for bonus points knowing that the weather was going to play a part on day four.
“The pitch flattened out, but I just felt that we got away from the simplicity of our game plan with the ball and gifted some runs with some bad balls.”
The Yorkshire squad are staying down south to prepare for their next assignment – Thursday’s Royal London Cup quarter-final against Essex at Chelmsford.
Yorkshire will have England players Adam Lyth and Jonny Bairstow available for that game although not Joe Root, who England want to take a breather.
Aaron Finch, Yorkshire’s overseas player, is ineligible as he did not take part in the competition’s group stage.