Frustration had spilled over among some home fans as the visitors maintained their shock lead at Old Trafford heading towards the hour mark and they made their displeasure known as Nani went off in the 58th minute to be replaced by Adnan Januzaj.
Nani has been criticised for a number of ineffectual performances this season after signing a new five-year contract in the summer, but Moyes insisted: "He is a regular and captain for Portugal so he is very talented.
"There were one or two decisions he might have made better, but he got us the (first) goal with a lovely ball. We have a lot of competition for places in the wide areas, incredible competition, and that is what we're looking for."
Moyes was keen to play down the significance of a victory which keeps United eight points off the lead and, following the midweek UEFA Champions League win over Real Sociedad, goes some way to atoning for their sluggish start to the new campaign.
United's familiar frailties were on show again in a turbulent first period in which Peter Crouch gave the visitors a shock third minute lead, then Marko Arnautovic took moments to put the Potters back in front after Robin van Persie had bundled home an equaliser.
Wayne Rooney flicked a 78th minute equaliser from a Van Persie corner then substitute Javier Hernandez proved United's hero two minutes later when he headed home a Patrice Evra cross - but Moyes was keen not to over-play the impact.
Moyes insisted: "It was a win in the Premier League. They are hard to come by and they are not easy.
"It was a big moment to win the game and hopefully we will continue to win games. If it's in the same fashion then we'll take it, but if we can make it a bit easier it will be great for the old ticker."
Defeat was hard to take for the visitors but captain Ryan Shawcross believes it was the type of performance which can stand Hughes' men in good stead for the rest of the season.
Shawcross said: "Obviously we're disappointed but it's great that we came to a big team and put in a performance like that.
"They (United) have struggled so far this season so of course we came here with more belief on the back of the poor results they've had. But they're still a great team and they showed that in coming back to get the victory.
"We've got a good run of games now, five or six that we should take points from. The gaffer has set us a target and we've got to achieve it. It's going to be hard but we can take some belief from a performance like that."