The result left the Hatters 14th in League One, eight points away from the play-off places ahead of next Saturday’s trip to Northampton Town.
“It was a game of spells and what I learned about this league is that when you’re in those (good) spells, you have to make them count and we didn’t,” said Wilshere.
“A lot of things I saw in the first half were positive. I also learnt a lot about the place, the players, what they’re feeling, (but) we’ve got work to do.”
Wells, who has now missed two penalties this season, took the spot-kick despite Gideon Kodua also being on the pitch, having scored one against Blackpool last month.
Wilshere said: “In that moment, it’s down to the player who wants it and Nahki fancied it. He had courage, he wanted to do the right thing.
“He was instrumental in a lot of the good things we did and we need him.”
Asked about his sides’ failure to create and convert chances, he replied: “It’s not that we’re not winning the ball back high enough or not creating opportunities, we are and we have to use that.
“Is it a mentality thing? It could be, finishing is one of the hardest things to do in football so we have to find a little bit more quality or calmness when we’re in those areas.”
Wilshere described his welcome from supporters when he walked out onto the pitch before kick-off as “really special”.
He added: “I didn’t know what to expect when I went out. They were amazing. It was tough at times (for them) and they’re right to be frustrated but stick with us.”