It was the same scenario - which left Sussex with a point - on Friday, when their match against Kent at Canterbury was washed out.
Gillespie said: “It’s been another frustrating day. We keep saying it but we can’t control the weather. Considering we have had such wonderful weather it has been frustrating, not just today but on Friday.
"All we can do is prepare as well as we can, which the boys have done. It’s just about staying on positives. We have to adapt. And that’s been our real buzzword this season, adapting to situations and conditions and whatever is thrown at us. We will attack everything head-on."
Commenting about the return to fitness of Sharks paceman Tymal Mills, Gillespie added: “It’s nice to have all your players fit. We still don’t have Stiaan [van Zyl] available, unfortunately, but to have Tymal fit again and available is fantastic.
“It was tough on Ollie [Robinson] to miss out in Canterbury, where we went for the extra pace of Tymal, who has had a bit of a lay-off. We just have to decide on the most effective line-up on the day. I don’t like to chop and change too much.”
Looking ahead to an important game against Gloucestershire on Wednesday, Gillespie added: “Michael Klinger is a fine player and he’s done very well for many years for the various teams he’s played for. It’s up to our bowlers to come up with their thoughts and plans and be really clear about them, so we can implement our skills.
“Gloucestershire play conditions and adapt quickly. They know their game. Under coach Richard Dawson they do their research really well, so we must be equal to the task.”
Hampshire coach Craig White said: “It’s been a very frustrating day. With the situation we’re in we need as many points as we can get.
“We’re not mathematically out of it but we need to start winning. We need to get on a roll. We need to win against Somerset away on Wednesday and at home against Kent on Friday. We have to stay positive. Everyone is beating everyone at the moment so it’s anyone’s guess who will make it into the top four.”