Silva pulled up after just 10 minutes but the hosts seemed to cope with the departure of the Manchester City midfielder and went ahead through Sergio Ramos on 25 minutes.
Cesc Fabregas then had a penalty saved by Hugo Lloris just before half-time, but after Arbeloa also went off with a muscular injury minutes into the second period, the visitors took control of the game and finally got the equaliser they deserved with the last attack of the match as Olivier Giroud rose to head in Franck Ribery's cross.
"The injuries were an immediate misfortune because it prevented us from managing the changes," Del Bosque said.
"There haven't been any muscular injuries in my four years here and so to have two I am sorry about."
The draw leaves both sides tied at the top of Group I with seven points from three games, but Del Bosque refuted the suggestion that the group will be decided when the two meet again in Paris in March.
"We have played only three games," he added. "In the first half we had control of the game and perhaps we lacked a bit of penetration with the missed penalty by Cesc and the other chance that Pedro had.
"The home and away games against France have always been dangerous for us. What will happen with the rest of the games I don't know, it would appear March already will be important, but we can't take anything for granted with the other teams in the group as they will all aspire to be first."
France boss Didier Deschamps was delighted with how his side responded from going behind to end up dominating in the second half, but he also lamented a poor decision by the officials that saw Jeremy Menez's header wrongly ruled out for offside.
"In the first half we suffered, we defended well, but they didn't give us the ball and we weren't able to attack practically at all," Deschamps said.
"In the second half we had more presence, we were liberated and created more chances. You can't also forget that they ruled out a legal goal.
"We had to be magnificent, we were playing the best team in Europe and the world. The players have seen the recompense for their efforts.
"If this match brings more enthusiasm and confidence to the players then good, but we are not the best just because we have drawn with Spain.
"We are a young team, we haven't done everything well but we have character and a lot of margin to improve."