Di Canio quit his post as Robins boss on Monday, citing off-field events as the reason for his resignation.
Piccareta took charge for Tuesday's clash with Tranmere Rovers, which Swindon won thanks to a Gary Roberts brace and an additional goal from James Collins.
That result moved Town to the top of League One, but Piccareta has confirmed the intent of Di Canio's former backroom team to still join the Italian in leaving the promotion hopefuls.
Speaking after the game, he told reporters: "We leave the team top of the league in League One but it's the outcome of the fantastic job that Paolo Di Canio and the team and ourselves as technical staff have done in the last two years.
"We are here for Paolo Di Canio and we will follow him everywhere even if he coaches at Real Madrid or Luton Town because we are a team and we have shown these past two years that if you have a strong team and all the people involved are a strong team you can make a fantastic achievement."
Di Canio led Swindon to promotion from League Two in his only full season as boss.