"We'll keep working at it. I suspect that in the second and third week, as the race gets harder, riders get tired, there are hard stages to go and the Tour will open up more and more," he said on Tuesday's rest day.
The Australian is one minute 53 seconds down on Wiggins after Monday's key time trial in Besancon and also under threat from the Briton's team mate Chris Froome, who is only 14 seconds behind him overall.
Evans admitted that Team Sky's performances, both in the time trial and in the mountains made it necessary to attack from now on to make up for lost time.
"When you're two minutes down, you have to make moves," he said. "There is not a great deal else to do. We will have to think about different plans. But I think things will really change in the third week among the top 10 riders and that we'll see a reshaping in the classification.
“My strength is consistency. A lot can happen still. I didn't write the script so we'll kept writing in till the end," he added.
Some think Wiggins's only potential weakness lies in his handling of the third week of a Grand Tour, a flaw the Briton himself played down.
"Evans has more experience than I do but this is my fourth Tour de France going for the GC and each year is going much better," Wiggins said.
Given the strength of Team Sky, the title-holder made it clear he hoped for other Tour contenders like Italy's Vincenzo Nibali to join forces with him to try to upset the British outfit.
"Now they have to make bolder moves, which normally plays more in my favour," Evans said. "Sometimes, unfortunately, riders ride conservatively because they're satisfied with their position."
The Australian made it clear he would be battling all the way to Paris.
"I'm sure I can still win the Tour, otherwise I would quit and return home to play with my son," added Evans, his adopted boy in his arms.