The centre-back insists the duo's recent barbed exchange on Twitter was blown out of proportion by the media
Pique sarcastically claimed he was watching a "comedy film" after Madrid were awarded a controversial late penalty against Elche, prompting Arbeloa to issue a retort.
The former Manchester United man has stressed there is no bad blood between the Spain team-mates, claiming the situation has been exacerbated by the media.
"I'm not sorry about the Twitter post, but I think it's all been blown out of proportion a bit," Pique was quoted as saying by La Vanguardia.
"I made a comment on a situation, I was answered by a Real Madrid player and suddenly there's talk of a big conflict when I didn't send the message specifically to him and Alvaro didn't send the message specifically to me.
"There are no hard feelings or bad blood between us."
Pique and Arbeloa both featured for the full 90 minutes in Spain's 2-1 World Cup qualification win over Belarus last Friday.