The Chelsea centre-back feels the 1-0 win over World Cup holders and European champions Spain last season and the 2-1 triumph over Brazil this week has highlighted England's credentials.
Cahill insists the victory against the five-time world champions is a "statement of what we can do" but knows there is still much to learn and improve upon.
Asked if England had anyone they should fear at the next World Cup, Cahill replied: "I don't think we do now. I thought we did fantastically well against Brazil.
"We also played and beat Spain, which was a more resilient performance when we defeated them here.
"We have proved we can mix it here with the big lads, so I think we have nothing to fear.
"I don't know why we have been doing well against the big teams. Naturally everyone who plays in a big game raises their game a little bit. Why that is, I don't know.
"Against Brazil was very positive. I thought there were a lot of good individual performances and we played really well.
"It was a statement from us of what we can do, probably one of the better performances I've been involved in at Wembley, but we are still learning, we still have a young squad."
Cahill is encouraged by the young talent emerging and cementing its place in the England squad.
He said: "We've got a mixture of experience and youth, but more youth if you look at the squad. We've got loads of players aged under 25.
"It will stand us in good stead if they keep learning and keep progressing.
"A lot of them have played in big football matches and big games for their clubs and hopefully they will keep improving."
Cahill was at fault for Brazil's goal as he lost possession, allowing substitute Fred to score, but overall was pleased with his performance.
He said: "I was distraught about the goal. It was out of character. It was just a bad decision but that's something I need to learn from.
"If I learn from that then great. Taking the positives from the game, I thought I played really well.
"But the nature of my position means you can play well for 89 minutes and make a mistake against sides like Brazil and you get punished.
"It spoilt the night a little bit for me but thankfully not for the other lads, so the most important thing is we won.
"I thought we showed character after that, personally to forget about the mistake and go on, and for the team, we showed character."
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