The Gers chief banished the veteran 37-year-old from his first-team squad following a meeting to discuss the 2-0 loss to Celtic.
Miller subsequently played and scored in a 3-3 behind-closed-doors friendly against Morton last Saturday during the international break.
And, after the pair sat down for clear-the-air talks this week, Caixinha revealed that they have now put their differences to one side.
“[He reacted] with full respect,” Caixinha said about Miller’s exclusion from the squad.
“He’s a senior player and he understands these things. We spoke and we clarified everything regarding those decisions.
“Sometimes it’s important to justify your decisions. Other times, I don’t have to justify anything. But we clarified everything.”
Aberdeen boss Derek McInnes believes his team can cause a major upset by knocking Burnley out of the Europa League.
Liverpool say plans for the redevelopment of the Anfield Road end are on track but building the new training ground takes priority.