Real sealed their first title in five years by beating Malaga 2-0 at La Rosaleda on 21 May, dashing Barcelona's hopes of securing a third successive title.
The Catalan giants came from 2-0 down to beat Eibar 4-2 on the final day, but finished three points behind Real on the La Liga table.
Iniesta dismissed suggestions that Barcelona's poor first-half showing against Eibar was because the players were distracted by the scoreline in Madrid's match against Malaga, with both games having kicked off at the same time.
"Well, we won. We did our homework, but Real Madrid were better than us. Congratulations to them," the Spain international was quoted as saying by Goal.
"We didn't miss because of [being distracted by Real's match]. We won. All the rest is irrelevant. It's a shame it wasn't enough.
"We knew [the Madrid score] at half-time, but we didn't know apart from that. We did the job, but we couldn't depend just on ourselves, it was out of our hands."
Barcelona still have a Copa del Rey final to look forward to against Deportivo Alaves, and Iniesta said the Barcelona squad was determined to give Luis Enrique a positive send-off.
Enrique will end his three-year reign as Barcelona manager after the match, with the club having already begun the search for a replacement.
"Everyone is grateful for what Luis Enrique did and now we are going to fight against Alaves next week to finish the year as great as possible," Iniesta said.
Enrique, 47, has led Barcelona to two La Liga titles, two Copa del Reys and one European Cup.
Reports have suggested that Athletic Bilbao coach Ernesto Valverde, who is out of contract at the summer, is the favourite to take over at Camp Nou.