Guus Hiddink's men will look to avenge last season's Champions League last 16 exit when they take on French champions Paris Saint-Germain at the same stage this month, while they host Manchester City in the fifth round of the FA Cup.
Chelsea are on a nine-game unbeaten run in the league under Hiddink but have drawn six of those fixtures.
"We've had too many draws to climb the table. The Newcastle game is a very important one where we have to get the three points," Courtois told the club's website.
"After that we play in the Champions League and FA Cup against two great sides and we have to try to win those games because the only way to save our season is to reach the final in one or both of them."
Chelsea are 17 points away from fourth-placed Manchester City with 13 games left, but defender Cesar Azpilicueta has still not given up hope on qualifying for next season's Champions League.
"Obviously every time we don't win and there is one game less, there is less chance to get into the top four. We will see where we are with five-six games in a row and see whether we can get there or not," Azpilicueta told British.
"We are trying and will always try to make it. We also have the path of winning the Champions League (to qualify) and we have a tough game coming up against PSG. We will try both ways to get into the Champions League this season."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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