The defender is under no illusions as to the importance of the former Liverpool man, who has signed an extended contract, while also hailing record signing Gareth Bale
The 32-year-old signed a new deal until the summer of 2016 with Madrid earlier in January and the full-back is delighted that Alonso has decided to stay on for two additional seasons.
"It would have been a blow if he'd gone. There is no other player like him in the world to replace him," Arbeloa told the club's official website.
"It is great news for everyone associated with Real Madrid and for him too, so everyone is happy."
The defender also briefly discussed the form of Gareth Bale following the Welshman's appearance in the 2-0 Copa del Rey win over Osasuna on Thursday, enthusing: "He did well and we're glad that he is with us."
Madrid resume action in La Liga on Sunday away against Espanyol.