The centre-back, 28, was jeered by a section of Spain fans during Saturday's Euro 2016 qualifier win over Slovakia, and was subjected to similar during the previous internationals break.
"The last thing I would do is leave the national team," he said.
"I won't change regarding club rivalry. I always wish Real Madrid to do badly."
It was reported that England's friendly in Spain on 13 November was moved from Real's Bernabeu Stadium to Alicante because of concerns over the possible negative reaction to Pique's involvement.
In June, the former Manchester United defender sarcastically thanked Colombian rapper Kevin Roldan for playing his part in Barca's success last season.
The performer posted photos on social media of Real team-mates celebrating Cristiano Ronaldo's 30th birthday in February just hours after a 4-0 defeat by Atletico Madrid. The players were consequently criticised.
Barcelona went on to win the league, Copa del Rey and Champions League.
"I don't regret anything that I have said and I would repeat it a thousand times and more," added Pique.
"I am like that, I want Madrid to always lose. That is the sporting rivalry that has always existed in Spain."
Barcelona defender Gerard Pique will stick by his anti-Real Madrid stance and continue playing for Spain despite being booed by supporters.