The newly-promoted Whites broke their transfer record by spending £26m on the Spain international forward.
A cash-strapped Valencia were desperate to offload the 29-year-old, who scored 59 goals in 220 appearances during a five-year stay at Mestalla.
It was Leeds who stumped up the cash for a player who famously spent time on loan at Bolton Wanderers as a youngster.
Rodrigo was linked with Barcelona last summer, and former Los Che sporting director Subirats believes he would have been disappointed not to join one of Spain's big clubs.
Speaking to Tribalfootball, Subirats said: "Finally, Rodrigo has gone to Leeds but not for the price that Valencia had been hoping for. But these are difficult times now, economically speaking, for the club.
"I don't believe that Leeds is really the best choice of club that perhaps Rodrigo would have liked to have joined.
"Regarding Rodrigo, in theory, I think he would have liked to have gone to one of the bigger clubs in Spain, which was on the cards before."
Nonetheless, Subirats believes the experienced Rodrigo can enjoy success in Yorkshire after he scored his debut goal against Manchester City before the international break.
"However, Leeds have just been promoted to the Premier League and are going to be creating a good project for this coming season. Anything could happen!
"Ferran Torres at Manchester City is an investment with good prospects regarding future success, but perhaps buying Rodrigo carries more risks because of his age and possible tendency to get injuries in the past. However, logically speaking, Rodrigo is a very important player. Perhaps not for 4 or 5 years… but I think he could do well for Leeds for his first couple of seasons (or so) there."