England supporters caused controversy last November when they chanted 'F*** the IRA' during the team's 3-1 victory over Scotland at Celtic Park.
Even though the Football Association (FA) liaised with fan groups after the game to try to prevent such chants happening again, they were heard during England's 1-1 draw at the Juventus Stadium in Turin.
Chants of 'no surrender' were also occasionally heard in Italy.
Any repeat during England's next match against Republic of Ireland in Dublin on 7 June could prove inflammatory and Hodgson wants to hear them no more.
"I'm very keen that we get the support that we get. I love the fact that our fans come (to matches) and there's no way I can justify or be glad about any political chants of that nature," the England manager said.
"We can only hope that in some way we can put that right before we go to Ireland because the last thing we want in Ireland is anything other than a very good football match which again puts us to the test, like the Italy game has done."
Hodgson wrote to England fans before Republic of Ireland visited Wembley two years ago, asking them to refrain from singing songs 'of a religious or political perspective - which could cause offence to our visitors or fellow fans'.
The move appeared to pay off as 'no surrender' was rarely heard during the match at Wembley and there were no arrests for football-related violence.
The last time England played in Dublin 20 years ago, crowd trouble caused the referee to abandon the match after 27 minutes.
After the win in Scotland, the FA made it clear it was unhappy about the chants.
An FA spokesman said after the match in Glasgow: ''We apologise for any offence caused by a section of the England support at the match with Scotland. The FA does not condone inappropriate and offensive chanting and intends to meet with supporters' groups to discuss the wider issues.
''We have consistently urged supporters to show respect and not to chant songs that could be regarded as insulting to others - particularly from a religious or political perspective.''
