Hodgson's men found themselves in the ascendancy in the shoot-out when Riccardo Montolivo missed Italy's second kick and Wayne Rooney scored the next to put his side 2-1 up.
However, Italy slotted home their next three kicks while Ashley Young's effort come back off the crossbar and then Ashley Cole saw his attempt saved by Gianluigi Buffon. Hodgson told Radio Five Live: "Anyone can miss a penalty. They were not nonchalant, Ashley Young's smashed against the bar and Ashley Cole's was well saved by Gianluigi Buffon."
He continued: "A player's reputation should not be forged on a penalty shoot-out, their reputation should be forged on the four games and in those four games we have not lost."
Hodgson also praised the overall effort of his men.
"We stuck to our guns right until the end and the players should be very proud of what they did," he said.
"I have learnt a lot about the players and their determination and dedication to the task and the fact they are so keen to play for England.
"There were some heroic performances not only tonight but also in the previous three games."