The Three Lions are aiming to reach their first semi-final since Euro 96 but, in order to do that, England must create their own little bit of history.
Away from Wembley, they have never beaten a major nation in the knockout stages of a tournament of any significance.
Manager and skipper have both called it a 50-50 game but, with the margins so fine, they are determined nothing should be lost for lack of effort.
"Someone is going to lose and whoever loses is going to be very sad," said Hodgson.
"We can't do anything to change that.
"What we can do is make certain we have no regrets at the end of the game."
For Gerrard, the plea was even more desperate.
Now 32, the England captain has spent his entire professional life being hailed as one of Europe's finest midfielders.
He has dreamt of achieving glory on the international stage, yet all it has brought him is pain and misery.
"Since I made my England debut I've dreamed of doing well in these major tournaments," said Gerrard. "Up to now that hasn't happened.
"There's another chance to do it here and, because of the hurt and pain I've been through before, I'm hoping it'll be different this time.
"I'm going to give it everything I've got to try and make it different this time.
"I'm sure there are a lot of players who are thinking the same thing.
"This is a fantastic moment for this team and this group of players.
"It's important we grasp it and we don't go home with any regrets."
For the second game running, England opted to complete preparations at their Krakow base before flying into Ukraine for a brief public walk on to the pitch where their destiny will be determined.
With no late injury scares, Hodgson is set to stick with the side that started against Ukraine on Tuesday, meaning Andy Carroll continues as deputy to Danny Welbeck.
Three times on the trot during Sven-Goran Eriksson's tenure, England bowed out at the quarter-final stage.
Gerrard was involved at Euro 2004 and the World Cup two years later, when hopes were dashed on penalties, the pain inflicted by Portugal on both occasions.
"Once you get to the quarter-final stage of a competition and you can see what's in sight, you start to dream," he said.
"To lose any quarter-final match it hurts so much.
"It's a massive game because you're so close to where you want to be."
Gerrard's influence is going to be enormous for a couple of reasons.
The 32-year-old has responded to the captaincy just as Hodgson would have wanted, delivering a succession of inspirational displays that have earmarked him as England's player of the tournament so far.
However, the Merseysider will also know it is his area of the pitch where the battle for supremacy is likely to be decided, where Italy playmaker Andrea Pirlo will look to exert his influence.
"I'm enjoying the tournament," Gerrard said. "I'm playing at a good level.
"But there's a lot of hard work and good performances needed before I get what I want out of this tournament."
If the game was decided purely on playing ability, England would probably edge it.
However, their opponents have an 'X' factor in their favour, which is why they have won four World Cups compared to England's one.
When their backs are against the wall, Italy, just like Germany, tend to find a way out of trouble.
"I would like to think we in England have a lot of their qualities," said Hodgson.
"What they have over us is that they actually use those qualities, one of which is finding a way to win even when, at times, they haven't looked anything like.
"We have to try and break the hoodoo. 1966 is a long time ago."