Luis Suarez's late strike condemned Hodgson's side to a second successive 2-1 defeat after Wayne Rooney had cancelled out the Liverpool man's opener in the 75th minute.
The upshot is England needing to win their final group game against Costa Rica and hope Italy can defeat Costa Rica and Uruguay to have any chance of reaching the next phase.
"We are devastated," Hodgson told ITV after the game. "We believed we could do enough to get a result in this game.
"Having worked so hard to counter that first goal, I thought we would go on to either win the game or at least draw it.
"I thought we did enough to get the draw that we would have needed."
As was the case against Italy on Saturday, England were left to rue their inability to apply an end product to some solid approach play.
"it doesn't matter how many times you get the ball into the opposing penalty box, it's how many times you put it in the back of the net," added Hodgson.
"On both occasions, we have not done that enough."
