Goals from Daniel Sturridge, Gary Cahill and Phil Jagielka sealed victory for Hodgson's side at Wembley in their last match on home soil before this summer's showpiece tournament in Brazil.
After what Hodgson described as excellent training camps at St George's Park and in Portugal Hodgson was asked if things were too good to be true ahead of the World Cup.
"Yes, that's probably right," the England manager said.
"And that is why I am very cautious. I hope my feet are on the ground, I know the players' feet are on the ground.
"You have to be satisfied when things go well. Portugal went well, St George's Park went well and we got the result we wanted against Peru.
"But it doesn't win us games in the future. It just means that we will have a nice couple of days before we start working again.
"It's just one small step on the journey we are taking so we need to keep working and keep concentrating."
Earlier on Friday it was confirmed that Prince Harry will attend England's game against Costa Rica in Belo Horizonte on June 24.
Following the win over Peru, Prince William - who is president of the Football Association - visited England's dressing-room to congratulate the players and wish them luck for the World Cup.
"We always knew the Prince would come in (to the dressing room)," Hodgson said.
"He is an enormous supporter of the Football Association and the England team.
"I was happy that he came into a happy dressing room. It was really nice to see him. He had a long chat with the players and wished us all the best for Brazil."
Hodgson confirmed Luke Shaw should be fine for the pre-World Cup training camp in the United States and also said Phil Jones and Alex Oxlade-Chamberlain have recovered from injury despite the pair missing Friday's game.
Hodgson also allayed fears over Leighton Baines' fitness after the Everton left-back was replaced by team-mate during the second half of the victory over Peru.
"He suffered a bit of cramp and that made us cautious so we took him off," Hodgson said.