The Blues earned the point against the Premier League leaders despite losing Moises Caicedo to a first-half red card.
"I’m proud," James told the club's website. "The team is so young, but we went toe-to-toe with the team at the top of the Premier League at the moment.
"We didn't show fear and we tried to come out to win the game. Unfortunately we weren’t able to do that, but there were a lot of positives to take from the game.
"We knew the game was going to be tough, but to be honest it was a game we felt we probably could have won. It was difficult to only walk away with a point considering how well we did.
"We played 60 minutes with 10 men, having to cope with all of their players – they are a very good team, they’re the league leaders at the moment. We went toe-to-toe with them, so we have lots of good things to take away.
"We started sharp, we had a few early half-chances, but the game got more difficult when we went down to 10. We made a few changes and they were coming forward a lot, but we still felt we had the players and the quality to hurt them when we got the ball. We tried our best, now we have to take a point and move forward."
We dominated
James also bullishly declared: "Our objective is always to win. This is Chelsea Football Club, the standards here are high. I think the result and the performance today speak for themselves and send a message to the other teams in the league.
"We dominated the whole game in every area throughout, with 11 men and 10 men. I think that was a big statement on where we are and what we're fighting for. We’ve come a long way and we’re building on result after result, and I think we showed that today.
"So I’m proud of the boys. It was electric here at Stamford Bridge today and we take a point and move forward."