The Romanian international, who joined from Steaua Bucharest over the summer, helped the visitors earn a 4-0 victory at Villa Park in the third round of the competition.
"For myself, it was okay," Chiriches told the club's official website. "I have to get better game by game but the performance of the team was very good.
"It's a great feeling, I tried to defend well and make a good performance for the team."
Tottenham welcome Chelsea to White Hart Lane in the Premier League on Saturday.