The 32-year-old Brazilian, who is moving to Williams next season after eight years at Ferrari, attended a Christmas lunch at the Italian Formula One team's Maranello factory along with Spaniard Alonso.
Ferrari president Luca di Montezemolo presented the Brazilian with an engine from the F2008 car in which he almost won the 2008 world championship, losing out by a single point to Britain's Lewis Hamilton.
Massa referred affectionately to team principal Stefano Domenicali as his "big brother" and said he would never forget the team's support for him after his near-fatal head injury at the 2009 Hungarian Grand Prix.
"It's in these circumstances that one understands what it means to be really loved and the atmosphere at Ferrari and the unique feeling of being part of the family is something I will miss a lot," the Ferrari website quoted him as saying.
He will not miss having to play a supporting role to Alonso, however.
"Thanks also to you Fer. We will meet again on track and this time I will try not to let you through," Massa told the Spaniard.