Hodgson has struggled to win over the critics despite losing just one competitive match - the Euro 2012 quarter-final against Italy on penalties - since his appointment 18 months ago.
Cahill told the London Evening Standard: "In our last four qualifying games, there was so much pressure on him and we went out and got the results we needed. There was a lot of talk about what would happen if we didn't win the games but he delivered.
"He has been a manager for so many years that he'd be used to the criticism that he was getting before. But when he delivers, he should be given the credit for getting the job done and getting us to the World Cup.
"We have had good results against top sides under Roy. Everyone is English so we should all get behind him and the England team. People should support him and the team to go and do well. Anything negative towards the country has a negative impact. If everyone gets behind us we can try to achieve something."
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