The striker, in the side owing to Andy Carroll's absence, scored in the first half to earn Alan Pardew his first win away from St James' Park.
"When you get a chance so early on the good thing for me was I had 90 minutes to make one count and fortunately I had the opportunity to put one away," Ameobi told Sky Sports 1.
"I won't get an easier chance, but I'm delighted to get the three points for the boys and the city after a tough Christmas.
"In the first half we dominated but were only 1-0 up and you never know in this league. We didn't get a second but we defended well and we needed to start keeping clean sheets."
Kevin Nolan praised man-of-the-match Chiek Tiote for his role in the win.
The United captain said of his fellow midfielder: "Tiote only gets better. The way he's taken to the league has been fantastic and he's been one of the buys of the season.
"On the field he's been a man mountain and he's a great signing, a great kid and hopefully he's got a great future with Newcastle."
Magpies boss Alan Pardew was delighted with the character shown by his players in edging out a narrow win.
"We worked hard and were disciplined and did the right things at the right times," he said. "A 1-0 away win, you take those and it's a good victory for us."
Speaking about Ameobi's early miss, Pardew added: "When you miss a chance like that you can go negative but we stayed in that positive mode and I thought we were deserved winners today.
"The group has shown all season we're of good character and some of the disciplines we showed today were first class.
"The most important message for a club as big as us is that we should expect to win every game, regardless of the opposition, and then we see where we fall."
Wigan manager Roberto Martinez was disappointed that his side had not managed to impose themselves on a game at home.
"It was a very scrappy game and we were poor, not up to the level we know we can achieve and there were a few reasons for that," he said.
"After a slow start we were starting to show a little bit of a threat and creating opportunities, but it was one of those games where the first goal was going to be very important.
"We couldn't find a way to be ourselves, to impose ourselves, and to keep the ball. It was scrappy and we were looking for a bit of hope rather than a controlled performance."
Martinez blamed the heavy festive fixture list for taking its toll on an injury-depleted squad.
"With the amount of games we've played, we try to play at a high intensity and Wednesday's performance took a lot out of us," he said.
"We have four important injuries and a suspension, so there's a lot of pressure on the players out there and they didn't have the energy to impose ourselves.
"Newcastle's goal came from our mistake and it's one of those games where everything went away from us."