Evans told BBC Sussex: "I don't think we're going out to Derby. I want to be in the fourth round, and I'm sure my players do.
"I'm sure Nigel Clough would rather be going to Swindon than coming to Crawley when he sees our performance."
Evans thinks victory over League One Swindon gives his team reason not to fear Championship opposition.
"We've deserved to go though. The quality of our play was outstanding. We had some huge individual performances which you're going to need," he said.
"We look forward to the biggest game in our history when Derby County come. Its not about Brighton 25, 30, 40 years ago. Derby are a huge, huge club, riding high in the Championship, aiming for the Premier league."
Crawley are currently second in the Blue Square Bet Premier chasing promotion to the Football League for the first time ever.
But Evans also wants to pursue the FA Trophy as they begin their campaign at home to Blue Square Bet South Dartford this weekend.
"We'd be disappointed if we suffered a negative reaction in the Trophy," he added. "We cannot win the FA Cup, we can win the Trophy. But we can't win it if we don't beat Dartford.
"I don't think we can treat our opponents lightly. I watched them two weeks ago against Woking and I thought Dartford were outstanding in spells".
Source: BBC Sport
Source: BBC Sport