The Northern Ireland boss apologized for saying that women are more emotional than men.
He apologized on Wednesday for the offense he caused.
"I am an advocate for the women's game and passionate about developing opportunities for women and girls to flourish," he said.
They were unable to qualify for the Women's World Cup because they conceded four second-half goals.
He told a news conference that he felt England were struggling at times to open up until the psychology of going 2-0 up in the women's game came into play.
If you go through the patterns, you will see that when a team concedes a goal, they concede a second one in a very short space of time.
It happens right through the whole spectrum of the women's game, because girls and women are more emotional than men. They take a goal that is not very well.
The match was attended by a crowd of over 15,000 people, a record for a women's match in the country.
I apologize for my comments made in the press conference last night.
Last night was a special occasion for the women's game in Northern Ireland and I am proud to manage a group of players who are role models for so many girls and boys.
The former goalkeeper for England, who played 50 times, said that Shiels had to take responsibility for knowing the value of words.
The five minutes after you concede a goal, not just in women's football, but also in men's football, you're more likely to concede a goal.
It's a strange comment to just generalise that to women.
When you give a news conference after a big game, it is important to make sure that you are speaking sensibly and are aware of the message that your words can carry.
Wright said that Shiels was talking foolishness.
Yvonne Harrison is the chief executive of Women in Football.
Harrison told the news agency that he felt like he had gone back 30 years when he heard a man talk about women being too emotional.
It is something women have had to face for years and years in society.
It is not easy to take when your team has just been beaten by a very strong Lionesses team and you have all the media on you.
England went up by a goal in the 26th minute but had to wait until the 52nd to add a second.
We tried to slow it down to give them time to get over it. That is an issue we have.
Not just in Northern Ireland, but all of the countries in the world.