The match was tightly contested throughout, with few clear chances for either side. City eventually made the breakthrough in the final quarter of an hour through a decisive finish from Antoine Semenyo, leaving Chelsea with little time to respond.
James, who returned to the starting XI after injury and operated in midfield, felt the game was decided by fine margins.
"It's disappointing to lose," James said. "If you take a step back and look at the game, not the scoreline, we matched them and went toe-to-toe. They had more of the ball in the first half but didn't really hurt us, and then they scored from a half-chance in the second."
He added that effort and commitment were not in question from Chelsea's side. "I tried everything and did everything I could. Everyone wanted to win. I can't question anyone's desire. We just didn't get the rub of the green."
James also praised teammate Levi Colwill, who has recently returned to the team after a spell out injured.
"Levi is huge for the club and the team," James said. "He's been a big loss this season, and since coming back he's looking really strong and helping us a lot."
With two Premier League matches remaining, Chelsea still have a chance of securing a European place, but James admitted the season has not met expectations.
"We need to rest, recover and get back on the training pitch to prepare for Spurs," he said, referring to their next match against Tottenham Hotspur.
"We've underperformed this season. I want to apologise to the fans for the lack of results. It's been difficult, but I hope we can pick it up soon."
