Gillespie's men take on Northamptonshire Steelbacks at North Marine Road tomorrow (Tuesday), in the Royal London One Day Cup before their huge Roses derby clash against Lancashire on Wednesday.
The Aussie insists the squad remain confident of turning their limited overs fortunes around.
He said: "You can talk about our T20 form, but Lancashire lost six last season and won it.
"It’s not all doom and gloom. We’re very positive. The lads are in a fantastic place.
"Yes, we’ve lost a few games, but we’re talking well in the dressing room and communicating well on the track. The lads are very clear with what they’re trying to do.
"They haven’t quite got it right, but there’s a lot of optimism about our shorter form cricket.
"I know that people in the media and the public are worried that things aren’t going according to plan, but we’re very tight, feeling strong, and we’re focusing on the things that are allowing us to do well.
"The lads know what they’re trying to achieve, they’re researching their games and the opposition - the analysis is good.
"They are giving themselves the best chance. We are trusting them to go out and get the job done. And they will.
"The public don’t see what we see. They don’t see the lads putting the work in at training or listening in on the debriefs.
"It comes down to the fact that you’ve just got to have that belief and trust.
"I am really excited about our short form cricket because I see that we’ve got a really good squad, and we feel that we’re going to have an impact this summer."
Tomorrow's clash gets under way at 11am, with entry £16 for adults, £10 concessions.
Yorkshire Vikings 14-man squad to face Northamptonshire Steelbacks and Lancashire Lightning: Gary Ballance, Tim Bresnan, Karl Carver, Ben Coad, Andrew Hodd, Jack Leaning, Alex Lees (Captain), Adam Lyth, Steven Patterson, Liam Plunkett, Adil Rashid, Will Rhodes, David Willey, Kane Williamson.