The Yorkshire first-team coach was speaking after his side thrashed Northamptonshire by 271 runs at Wantage Road, despite conceding a first-innings deficit of 115.
The result briefly sent Yorkshire back to the top of the County Championship, although Middlesex – who have played one game more – returned to the summit a short time later by virtue of bonus points obtained from their ongoing game against defending champions Durham.
But Gillespie – who insists there is more to come from his title-chasing team – feels yesterday’s win proved Yorkshire have the spirit to challenge all the way.
“I thought this was a massive performance in terms of the character shown by our players,” he said.
“To be bowled out for 136 in 40 overs on day one and to concede a big first-innings lead, and to then come back from that, was an incredible effort really and I can’t speak highly enough of our lads.
“The way we responded showed a hell of a lot of fight, a hell of a lot of character.
“If you want to challenge for the top one or two spots in the Championship, then you need to put in performances like that and show that you can bounce back from poor sessions, poor hours, poor days.”
Although delighted with his team’s fighting spirit, with openers Adam Lyth and Alex Lees sharing a stand of 375 to help Yorkshire to 546-3 declared in their second innings before the visitors dismissed Northamptonshire for 160 yesterday, it was not a perfect display against the Championship’s bottom club.
Yorkshire will be conscious of the fact, if not concerned about it, that there have been passages of play of late in which they have not quite been at their sparkling best.
“While it was a good performance and a great win against Northants, there is still room for improvement,” stressed Gillespie.
“We weren’t as sharp and as crisp as we could be with the bat in the first innings, and also our disciplines weren’t quite there at times in the Northamptonshire first innings as much as we would have liked.
“We put down a couple of catches as well, so there are definitely areas we still need to work on.
“But the most important thing was the fight that we showed; Andrew Gale, the captain, asked the lads to show that and to try and find a way back into the game, and they most certainly did that, and it’s one of the best wins I have seen for a long time in cricket.”
If the groundwork for victory was laid by Lyth and Lees, whose stand was the fourth-highest for Yorkshire in all first-class cricket, then pace bowler Liam Plunkett applied the coup de grace.
After Tim Bresnan made early inroads with three important wickets, Plunkett showed why there have been calls for him to feature in the forthcoming Test series against Sri Lanka, returning 4-42 in yet another example of hostile fast bowling.
“Liam has just got absolute clarity in his role,” said Gillespie.
“That role is basically to run in and bowl fast for us and to hit the track hard – not to worry about however many runs he goes for.
“In the first innings at Northampton he went for 55 off eight, but we knew that he was running in and bowling quick and that the rewards would come.
“This season, from what I’ve seen, Liam has probably consistently been the quickest bowler in the country.
“There are some good fast bowlers around, but he’s certainly been bowling as fast as anyone.”
Yorkshire’s latest win was achieved without Ryan Sidebottom, the former England left-armer, who is struggling with an injured left hamstring.
Gillespie said the next Championship match against Nottinghamshire, starting at Headingley on Sunday, will come too soon for the 36-year-old pace bowler. “Ryan won’t be available for the Notts game,” he said.
“We just have to make sure that he’s 100 per cent because it’s a long season and we don’t want a guy going in less than 100 per cent and maybe re-injuring himself, because he’s too important a player for us.
“We will make sure he is bang-on right before he plays, but we don’t envisage he’s going to be out for six or seven weeks or anything like that.
“But, if it means that we have to wait for an extra week or so, then we’ll do that.”
Yorkshire return to action on Friday when they play Lancashire in the NatWest T20 Blast at Old Trafford (6.30pm start).
Final-day report and cricket scorecards: Page 22.