Pique voted in the illegal independence referendum in Catalonia and criticised the Spanish government for trying to shut it down violently, angering some Spain fans.
A large group of supporters jeered and insulted the Catalan centre back during a short training session at Las Rozas on Monday.
"When I've come (to the Spain camp) Pique has always had the same attitude, commitment and happiness," Bayern Munich midfielder Thiago told reporters on Tuesday.
"(The situation) saddens us because we come here to talk about football, I'm not here to talk about the life of anybody. It saddens me not to be able to be comfortable and talk about Albania (whom Spain play on Oct. 6 in Alicante)."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Thiago backed Pique to overcome any abuse from Spain supporters during the game.
"Pique's already played at the Santiago Bernabeu many times. He's used to hostile environments. He has the same attitude as always," added Thiago, who played with Pique at Barcelona until 2013.
"I've enjoyed watching him as a player and having him as a team mate and I love to be able to keep doing so."
Spain, Group G leaders, are bidding to seal a place at next year's World Cup in final qualifiers against Albania on Friday in Alicante and Israel in Jerusalem three days later.
Atletico Madrid midfielder Koke wants to put the issue to one side and focus on confirming Spain's presence in Russia.
"We always feel the support of the fans. Alicante loves the national team a lot and I'm sure we will feel their affection," he said.
"The atmosphere in the dressing-room has not changed. We are focused on winning and reaching the World Cup. We're studying our opponents, it won't be easy to win but we can almost seal qualification (against Albania)."
(Editing by Ed Osmond)
