"The first half was very good for us, we played really well. It was a good performance and we needed that," Courtois told the club's website (www.chelseafc.com).
"Obviously when a manager goes it's a difficult situation. Everybody is sad about what happened because we haven't played well and won games, so we have to react and do better.
"We don't play to lose but we are responsible as well, we have top players so we shouldn't be 15th in the league."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The Belgium international said the team, who are in 15th place after 17 games, had the quality to perform a high level and believes things would get better under Hiddink, who will begin his second stint as Chelsea's interim manager.
"He (Hiddink) was here before, he did very well and I think he's a very good manager," Courtois said. "Hopefully together we can climb back up the table and we're looking forward to starting working with him.
"Whatever has happened (with Mourinho) stays in the past and now we want to work hard with the new manager to get a good result against Watford."
Chelsea play seventh-placed Watford on Saturday, before travelling to Old Trafford two days later to play Manchester United, managed by Hiddink's countryman Louis van Gaal.
(Reporting by Nayan Das in Bengaluru; editing by Sudipto Ganguly)
