Wilshere was pictured smoking outside a nightclub last week and he then caused controversy in the build-up to Friday's game at Wembley by wading in to the argument over the possibility of Adnan Januzaj playing for England.
Hodgson defended Wilshere's right to say that "only English players should play for England" and backed the midfielder to perform at Wembley in the forthcoming qualifiers against Montenegro and Poland.
"We wouldn't allow ourselves to be distracted by such a minor issue," the England manager said.
"He's put everything behind him. It's not affected him one bit on the field.
"I think England will get a lot out of him in these next two games and for a long, long time to come.
"Jack is entitled to his opinion. The subject of nationalising players who have had no previous connection with England, who have never been here as a youngster and not gone through the English education system or the English footballing system, is a matter for a policy decision."
Wilshere was drawn in to a spat with England's South Africa-born cricketer Kevin Pietersen over his comments, but the Arsenal man has since claimed his point was misinterpreted.
Hodgson would not give his thoughts on nationalisation, but England captain Steven Gerrard appears to agree with the idea of foreign-born players turning out for the Three Lions.
"If players become available through FIFA rules, it's only right that the FA look in to it," said Gerrard, who will win his 106th cap against the Montenegrins.
"We need to try and gain every advantage we can to make the England team as strong as possible."
Another topic that threatened to cast a shadow over the do-or-die qualifiers concerned Harry Redknapp, who hit out at the Football Association in his recently published autobiography.
Redknapp criticised the organisation's hierarchy and also claimed he had received texts from a number of senior England players, including Gerrard, backing him to replace Fabio Capello.
Gerrard denied sending Redknapp a text, but conceded he would have supported the QPR boss had he got the job instead of Hodgson.
"I didn't text Harry Redknapp's personal phone. I have never had his (mobile) phone number," Gerrard said.
"I am a big fan of Harry. I had a conversation with Jamie (Redknapp), around the time when Harry was on everyone's lips.
"He was the favourite, it (looked like) it was only going to be a matter of days before he was going to be the new manager.
"I said to Jamie on the phone - send my best to your dad and if he gets the job we will all back him and we will support him."
Gerrard is still more than happy to work under Hodgson, however.
"I was absolutely delighted that Roy got the job because I have worked with him before at Liverpool," the Liverpool midfielder said.
"He made me (England) captain and I think I have played my most consistent football under Roy so I have a lot to thank him for."