Jan Kirchhoff hopes Sunderland "will be rewarded" for their effort in the coming weeks.
A goal from Sergio Aguero separated the sides, with Sunderland missing a host of chances that left them four points from safety.
The German defender was deployed in a midfield role alongside Lee Cattermole and Yann M'Vila, and impressed after a very difficult debut against Tottenham last month.
Encouraging performance
Kirchhoff paid tribute to the "power, strength and intensity" that Sunderland showed, but it was not enough to breach Joe Hart's goal.
The 25-year-old, who arrived from Bayern Munich in January, stated that Sunderland must "produce the same intensity" if they are going to start picking up points as they aim to escape the relegation zone.
"When you play on this intensity you can be a very strong opponent to any team in the world," said Kirchhoff.
"We have good quality and a good team with good players in the squad so we have to perform like this every week."
Lucky Manchester City
Kirchhoff felt that their "high quality" opponents were "lucky", and hopes Sunderland will have more joy when they come up against sides who "can't defend so well as City".
"They had one chance and scored, we a lot but couldn't and that is the game," he said.
Despite a positive performance from the Wearside team, defeat and other results have made their quest for safety even more difficult.
A win for Bournemouth and a draw for Swansea helped them move away from the relegation zone, meaning that Norwich are the only side in touching distance. The Canaries have 23 points, four more than Allardyce's side who remain in 19th place with 14 games to go.
Sunderland's next game is away to Jürgen Klopp's Liverpool on Saturday.