Accies lost their unbeaten start to the campaign as County sealed a 2-1 away win to book their place in the third round of the Scottish Communities League Cup. Billy Reid's side return to league duty on Saturday against Livingston, with the Hamilton squad eager to make up for their poor showing.
Kilday said: "I don't think the defeat will affect us mentally. We are a strong group and we have some good leaders in the changing room.
"We know we need to bounce back straight away and that is what we will be looking to do.
"Everybody has to pull together, the whole team has to play well because you can't have any passengers in this league.
"We had a good start to the season and we have to keep improving on that."
Accies could, and should, have put the tie to bed early on Tuesday night after James Chambers gave them a first- minute lead from the penalty spot.
The hosts were slack in the second half as County came storming back and Kilday admits: "It was very disappointing, especially after the start we made. To get the early goal and then lose the game so late on is hard to take.
"We beat them 5-1 a couple of weeks ago, but we knew it was going to be difficult on Tuesday.
"They came back in to the game and did well and we weren't good enough. We knew they would be up for it and we didn't do as well as we needed to."
lThe draw for the last 16 of the Communties Cup will be made on Monday, with the Old Firm, Hearts, Dundee United and Kilmarnock all entering the competition. Falkirk, who beat Stenhousemuir 3-1 last night, and St Johnstone, who were 3-0 winners over Livingston, will also be in the hat.