The Gunners went down 3-1 to the Villans at the Emirates Stadium but have since won four games in a row in all competitions, including a 1-0 home victory over North London rivals Tottenham Hotspur on Sunday.
"You heard some things from the stand during the Villa game that we should spend money," Arsenal's official website quotes him as saying. "But [on Sunday] everybody was calm and just encouraged the team to fight.
"We played well and that's always the best answer to the rumours and the criticism. We just kept clam and did our best. The derby is always important to win and we showed that we are a good team with good spirit and we showed we can defend as well.
"The manager (Arsene Wenger) said at the start that we should believe in ourselves and in our passing game. In the first half we did that fantastically and showed we are ready for the fight for the rest of the season."
Arsenal are currently fourth in the league table with six points from three matches.