Pepe Mel's men found themselves 2-0 behind inside the opening 10 minutes at the Etihad Stadium, and they were unable to turn the scoreline around despite Graham Dorrans halving the deficit.
The defeat ended a three-game unbeaten run for West Brom and leaves them just three points clear of the Premier League relegation zone.
Full-back Jones - who made his first start since February following a hamstring injury - said West Brom had felt confident of taking something from City before the game, but were undone by their poor start.
"In recent games we’ve been starting really well and that was the plan again here but it was poor from us, we’re really, really disappointed," he told the club's official club website.
"We obviously wanted to get something here. Sunderland came here and did well and we were positive we could do the same.
"It was a really, really poor start and to give these guys a 2-0 head start it was always going to be a hard night."
West Brom face West Ham at The Hawthorns on Saturday as they continue their battle for top-flight survival.
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