For all of the possession, passing and control displayed during Group B, Roy Hodgson's men have lacked a cutting edge despite the glut of attacking options at their disposal.
That proved costly on Monday as an organised Slovakia side held firm to secure a 0-0 draw in St Etienne, allowing Wales to usurp England at the top of the group and setting up a last-16 clash next Monday in Nice.
Portugal, Hungary, Iceland and Austria are the potential opponents for a match Cahill hopes things will belatedly all come together.
"The way we're playing we shouldn't fear anyone," the stand-in captain against Slovakia said at the Stade Geoffroy Guichard.
"I definitely feel like we are going to give someone a real beating soon. I hope that we do that.
"We have had six shots against us in the three group games and had over 20 shots ourselves against Slovakia.
"In terms of possession, dominating the game and creating chances, we have to be pleased.
"But we are also frustrated, we had so much possession in the second half and I have not been involved in such a one-sided game as that for a long, long time. To not get the win at the end is frustrating.
"But not finishing top may not be the end of the world. Who knows how Portugal's group will pan out? That group is very strange, Portugal could finish first, second or third.
"But if we do face them it will be far from an easy game. I feel that they have yet to get going and they have some great players."
England proved earlier this month that they have the wherewithal to beat Portugal, albeit they were without star turn Cristiano Ronaldo when overcome 1-0 at Wembley.
Hodgson's men will no doubt be keenly watching the conclusion of Group F on Wednesday to find out their opponents for next Monday's match, giving them a break that Cahill believes will be a help rather than a hindrance.
"Having a week between games could be good for us at this stage," the England centre-back said.
"It will freshen everyone up and people can shake off little niggles. We can also work on things some more in training.
"The tournament has been intense and played at a great pace. To have that little rest now will be positive for us.
"By playing on Monday, we will have longer to prepare for our opponents and that is important.
"We may play with different personnel or in a different way, so all the time the manager and staff have with us is vital. That's another good thing about the timing of the game.
"We are not shying away from the fact we wanted to finish top of the group and we know the next round will be a big game.
"But we will go out and play in the same manner as we have done in the last three matches because we have dominated all of them."
The break also gives Cahill the chance to recuperate after an existing hip complaint flared up during the first half in St Etienne.
It had looked like the 30-year-old may be forced off with the issue - a worry given he is one of only three out-and-out centre-backs in the squad - but he has allayed fears it could impact him when the knockout stage starts.
"I think it's good for me to have a week to shrug it off," Cahill said.
"I was struggling a bit in the first half, but the second half was okay. When you have the England shirt and armband on, you don't want to come off."