Victory over Benfica came in extra-time on Saturday, which included an almost two-hour suspension of the game on 85 minutes due to a thunderstorm.
Eventually, Chelsea won the round of 16 Club World Cup tie 4-1 on the night, with James among their goalscorers.
The captain later said: "We’ve come a long way. It’s difficult to be so close to the end of the match and then have a kick in the teeth.
"To pick yourself up, brush yourself down and score a few goals probably shows how far we’ve come, and everyone has played a part today.
"It was a very difficult game with a lot of interruptions. The climate wasn’t the best, the pitch wasn’t the best, it was hard to play, and we got into 85 minutes, and we stopped for a long period of time.
"It takes a lot out of the players to cool down and then restart that engine again, but we’re happy we got the job done."
On his goal, James said: "As I was walking over and I was speaking to the centre-backs, and I asked them what they wanted. They said a shot, cross or in-swinger, and I said no problem.
"When I got to the ball and saw the goalkeeper's positioning; he showed me too much of the goal. So I just decided to shoot and it went in."