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City were way below par in the first half and went in 2-0 down at the break after goals from Maxwel Cornet and Nabil Fekir.
There was a significant improvement in the second period, with City playing at a higher tempo and getting a goal back through Bernardo Silva.
“There were strong words not just him [Arteta], but from the players as well,” he said. “That is the best way to build a very good team.
“Of course, we are a good team, we won the Premier League last year but to compete in Europe against nice teams, good players, quality players, you have to something extra and I think it is a good point because we discuss at half-time and before the game as well.
“Of course we want to improve, it doesn’t matter how and we are going to work through the week to the following game.
“It is hard to explain [the performance against Lyon]. I think we didn’t start well. We start waiting to see what happens. When we wake up, it was so late, we concede two goals and in that competition, we cannot win like this. We pay for that. We hope for the next times it won’t happen."
With Pep Guardiola serving a one-match touchline ban after an incident at half-time during last year’s quarter-final defeat to Liverpool, it was Arteta who took charge of proceedings against Lyon.
Guardiola sat in the stands and cut a frustrated figure as his side played without their usual intensity and creativity.
But Fernandinho refused to use Pep's absence as an excuse, saying the preparations leading up to the match were as detailed as ever.
“No, I don’t think so because we worked well the last two days, focusing with him but you have your own style of play and we play with him the whole season,” he said.
“It was different. The first half was very poor from us and you have to forget it and if you have to analyse the game, you have to take the positive points.
“We did that, especially in the second half where we created chances and conceded less chances. We will try to do better in the remaining games.”
Shakhtar Donetsk and Hoffenheim played out a 2-2 draw in the other match in Group F, leaving City bottom of the table after the first round of matches.
But with five games to play, there's still plenty of time for City to ensure a safe passage through to the knock-out phase.
Fernandinho says he expects Group F to be tough and has called for the City players to show humility as we head to Hoffenheim in a fortnight.
"All of them they have quality players," he said.
"My point of view is a tough group, I never thought it was going to be easy and they show that tonight.
"We had a first half to forget with some mistakes by myself and after the second half, we try to take over, to recover the result but it was too late.
"We have to be humble now and go to Hoffenheim to try and win there and the other four games as well."
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