The Blues led 2-0 going into the 87th minute at the Madejski Stadium before two late goals from Adam Le Fondre earned the Royals a point.
But, despite the west London side having won just one of their last five games, Bertrand insists the dressing room remains together.
"We always have been [united], no matter what gets written in the papers," he told the club's official website.
"Some of it is laughable but we are all together and we fight for one another."
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"We were deflated afterwards, it felt like a loss, being 2-0 up and pretty much in control," he added.
"If anything we were looking to sneak a third goal but this is football and you come to a place like Reading and they are never going to sit down and let you win that easily. Unfortunately we let them back into the game.
"Especially in the Premier League, all teams never lie down and with good crowds behind them, especially if they get the next goal, it is always going to be difficult.
"Those last five minutes were always going to be crucial, and unluckily for us Reading managed to get the equaliser. It is something we will look at, analyse and make sure we come back better."
Interim manager Rafael Benitez has come under considerable pressure during Chelsea's recent run of poor form, but Bertrand believes the players must take responsibility for the results.
"The players are the ones out on the pitch," he continued. "When it does go wrong, in the case of all managers they take the blame, but we are the ones on the pitch trying to get the performances right.
"Playing for Rafael Benitez has been fine. It is another learning experience for me personally and I am trying to learn as much as I can."
The full-back spent a season on loan at Reading three years ago, and is confident that the Berkshire outfit are in good shape to avoid relegation.
"Of late they have put some good results together," he concluded.
"Historically they always come good towards the latter stage of the season, and they have quality players and quality on the bench as well, as they showed on Wednesday night. They have a fantastic manager and I think they will be alright."