Jose Mourinho's side crashed out of the Champions League on Wednesday night after suffering a 3-1 defeat at home to Atletico Madrid and the 21-year-old Belgian goalkeeper, who is on loan at the Spanish club, was one of the architects of their downfall.
Sky Sports pundit Neville, who commentated on the game, says he was very impressed with Courtois' display and while there is no doubt that Cech, 31, remains one of the best goalkeepers around - the club may need to drop him and recall the "special" new talent to Stamford Bridge this summer.
"He performed tonight like a keeper should perform," he said on the Sky Sports Champions League Podcast.
"Goalkeepers are so intent on punching and so intent on not coming for balls when I think they should to take the pressure off their defenders.
"He was dominating his box, taking responsibility for such a young goalkeeper and catching it when he came. Even on one in the second half when Demba Ba went up with him for a header - and I thought he got a little bit fortunate because Ba was entitled to go for it - he still tried to catch it under big pressure.
"For me, it was a big, big performance from him. He looked totally cold and clinical and in control. The most important thing was he wanted to dominate the game when he came out for the crosses.
"I would say it would be harsh on Cech. He was voted by the PFA, his fellow players, as being the best goalkeeper in the league this year - and I actually put him in my team of the season.
"But if you are talking about the future and grabbing a goalkeeper back who is going to play for you for the next 10 to 15 years then he just looks a massive talent.
"I think they would have to [bring him back] and that would potentially be harsh on Petr Cech because I think he's a top goalkeeper. He's maybe not at the level he was at in 2005, but still a very good goalkeeper.
"However, they look like they've got somebody special there."
To hear more from Gary Neville on Chelsea's defeat and the all-Madrid final - plus who Paul Scholes and Phil Neville are tipping to win the trophy - simply download the Sky Sports Champions League Podcast now.