England have crashed out of major tournaments on spot-kicks on five occasions in the last 22 years, a run that dates back to that devastating World Cup semi-final defeat to Germany in 1990.
Only once during that time have the Three Lions been successful, when they overcame Spain at the last eight stage of Euro 96.
Little wonder Hodgson wants his players to get their eye in, even though he is not entirely convinced what good it will do.
"We have used the time after training sessions to regularly practice and we'll obviously take it even more seriously now," said Hodgson.
"You hope one day it will make a big difference.
"But you can practice penalty shoot-outs until the cows come home, it's really your composure, your confidence, your ability to really block everything out and forget the occasion that means you score or don't.
"Sometimes we've seen the best players miss and the ones you think are not penalty takers are the ones that smash them in."
A quick look at England's squad triggers more cause for concern.
Of those who started Tuesday night's win over co-hosts Ukraine, only Steven Gerrard and Wayne Rooney are regular penalty-takers for their clubs and both have had periods where they have found the task somewhat difficult.
In 2004 Gerrard missed a penalty against Fulham that cost Liverpool their place in the Champions League. He also failed to score in the Carling Cup final shoot-out win over Cardiff in February.
And in the middle of last season, Rooney had missed with four out of eight attempts, although he subsequently converted six in a row.
James Milner scored one for Manchester City last season and, like Ashley Young, netted twice in an epic European Under-21 Championships semi-final encounter with Holland that finished 13-12 to the Dutch.
That represents a little good news on a subject that is something of a national obsession.
"It's going to be that way because we've lost important matches on penalties," said Hodgson.
"When you are working with the England national team the past is always going to weigh heavily because everything we do today is being compared with something that before.
"Unfortunately we have lost two very important semi-finals on penalties so I presume that's going to be there during all my time as national coach. Probably when a national coach comes 20 years hence he will be asked the same question as well."
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