The Blues scored a stoppage time equaliser to force a 1-1 draw with Manchester United on Sunday which was their sixth share of the points in their past eight Premier League outings.
2-2 draws with Watford and West Bromwich Albion and a scoreless stalemate with the Hornets last week has cost the reigning champions from moving into the top half of the table and goalkeeper Courtois is feeling the strain of failing to produce wins, especially with the Champions League Round of 16 clashes with Paris Saint-Germain quickly coming up.
"We've had too many draws to climb the table," Courtois told the club's official website.
"In other games, like against Watford and West Brom, we should have won, so it's a pity because we could have maybe been ninth or eighth but we are where we are.
"The Newcastle game next week is a very important one where we have to get the three points. We've had too many draws at Stamford Bridge and the supporters deserve a victory.
"After that we play in the Champions League and FA Cup against two great sides (Paris Saint-Germain and Manchester City) 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."
The Belgian added: "It's obviously very good that we're fighting back to get these draws against good sides like Manchester United and Everton, it's good for the spirit of the team, but we want to win games."