The Hammers found themselves 2-0 down at Upton Park before Ricardo Vaz Te's goal saw them fight back in the second half.
However, they were unable to find an equaliser as the visitors went on to claim a 3-1 win.
"I thought that in the first half we maybe showed them a little too much respect, although you could see in the goal the quality that they have," Downing told the club's official website.
"In the second half, we probably left it a bit late, but after the second goal we started to play and believe in ourselves. That's what will frustrate the manager and the players, that we left it too late on Saturday.
"We got plenty of balls into the box in the second half, got a good goal back and I thought we had the momentum. But then Man City hit us on the break and scored a quality goal to wrap it up."
West Ham continue their Premier League campaign on Sunday with a trip to Swansea City.