The Three Lions' spot-kick defeat to Italy at the 2012 European Championships - under Hodgson's supervision - was their sixth in seven attempts at the mini-game in major tournaments.
So as preparations continue in earnest for England's forthcoming World Cup campaign in Brazil, he is especially keen to see those players who suffer from what he calls a fear of "the next morning's headlines" cured.
The veteran coach, who this week names a squad to face Denmark in a Wembley friendly, confirmed players would be intensely drilled in scoring from 12 yards at their pre-finals training camp in Portugal, but conceded bringing a professional sports psychologist along could be similarly effective.
Speaking to Sky Sports' Footballers' Football Show, he said: "We are considering the possibility of inviting someone with us but it would have to be someone accepted by the group.
"I'm not sure shipping someone in to give the players a lecture will work. It will have to be somebody who gets to know them.
"I think there's a possibility that we should just be encouraging players to know their penalty, to practise their penalty.
"We might have one or two very confident penalty-takers, but there are others who are a bit less confident and it's a matter of how we get to them.
"We need to know that when they go up they are as well prepared as they can be.
"It will be about their character, their confidence and their ability to block out the next morning's headlines.
"If a psychologist can find a way to block that out then we'd be very, very happy."
Hodgson must submit his final 23-man selection for the Brazil finals on June 2 and, to ensure he has not left anyone deserving behind, he will give seven 'fringe' players the chance to prove they merit a place on the plane.
The Three Lions will train in Portugal's warm weather for five days in mid-May before seven players are cut from contention when England return to Wembley to play Peru in a friendly.
"We will definitely take 30 players when we go to Portugal and we'll keep those players until we play the friendly with Peru," he added.
"But (before Portugal) I'll name the 23 and then name the seven who, at that moment, are not going to be in the final 23.
"In that way I put my cards on the table a bit earlier than I need to.
"We're taking 30 players with us but several will know that, in my thinking, they've got to go there as standby players."
Once the 23-man squad is finalised, England fly to Miami for warm-up friendlies against Ecuador and Peru before facing Italy in their first World Cup group game on June 14.
- Sports & Recreation