Forest arrived with a 1-0 first-leg lead but were missing several key players, including Ola Aina, Callum Hudson-Odoi and Dan Ndoye, while Morgan Gibbs-White, Ibrahim Sangare and Murillo were not fully fit.
"If you look at our bench today, we brought three players in condition to play," Pereira said. "The others were injured and not in condition to help the team.
"We came here without conditions to compete for the final. We had one less day to recover and that makes a big difference."
Gibbs-White suffered a serious facial injury in Monday's 3-1 win over Chelsea and, despite being named on the bench, Pereira admitted he could not feature.
"No," Pereira said when asked if the midfielder could have played. "Morgan was not in condition to help the team."
Pereira said Forest's injury crisis made the task impossible against Villa.
"Aina out. Morgan out. Sangare out. Murillo out. Callum out. Ndoye out," he said. "Playing against Chelsea and then travelling again after three days, it was not possible."
Despite the heavy defeat, Pereira praised his players and supporters after Forest's European campaign ended.
"It is a sad and difficult day, but I am proud of my team and our supporters," he said.
Forest now focus on their remaining Premier League matches against Newcastle, Manchester United and Bournemouth as they battle to avoid relegation.
