He said 53-year-old Smith, who has also worked at Renault, Red Bull and Force India before joining Caterham in 2011, was ousted due to the team's struggle for pace this season.
It has been rumoured that, having started the project in 2010, this season could be Caterham's last season in F1 before team owner Tony Fernandes loses patience.
"The one comment I would make is that we should not take anything for granted," team boss Cyril Abiteboul said in Barcelona on Friday.
"Formula one is the pinnacle of motor sport. We need to deserve our position on track. It's not like once you are in there you should sit down and relax," he added.