The decisive moment arrived in the 80th minute, when Madueke cut inside and shot. His effort took a deflection on its way past the goalkeeper, giving Arsenal three points from a match in which clear chances were scarce.
Nottingham Forest manager Oliver Glasner felt the outcome was harsh on his side, who defended with discipline but could not turn their own promising moments into a goal.
“I think everybody feels that the result is unfair today but it is another defeat and a game where we can't score at the City Ground,” Glasner told Sky Sports.
“Defensively it was a top-level performance. A deflected shot and Arsenal take the win. But we had our moments in the game and it is important when you play the champions you take these moments. It is the same in every single game. Today the performance, the efforts, the spirit and the energy was on a really good level but the result is missing.”
Arsenal struggled to find space against Forest’s organised shape. Arteta acknowledged that the hosts were difficult to break down and said his players had to remain patient until an opening appeared.
“We knew the margins would be really small. They are extremely well coached and organised,” he said. “The longer the game goes on they gain more belief. We had to be so patient - and clinical when we got the chance.”
Arteta also pointed to the chances Arsenal created after the interval, while admitting the team needed to make more of them.
“We have another three big chances that should be goals. That is the difference, you have to be clinical. If we keep generating them, they will come.”
The Arsenal manager praised the impact of his substitutes, naming Madueke, Jurrien Timber, Mikel Merino and Viktor Gyökeres among those who helped change the game.
“Sometimes you can get frustrated with teams who are difficult to break down. First half we didn't have a shot on target and that's something we discussed,” Arteta said. “We had another two big ones in the second half but the only one on target we had was a little deflection and it's in.”
Madueke said Arsenal had expected a difficult afternoon and needed to dig deep.
“They make it so difficult for you. It was a tough game. We're really happy all together. We showed grit and determination and showed a champion spirit,” he told Sky Sports.
The winger added that Arsenal’s belief had grown compared with last season, when similar matches might have slipped away.
For Forest, the frustration was compounded by another home match without a goal. Glasner urged his players to stay united and build on the defensive display, but the result left them with no reward for a performance he believed deserved more.