Malcom had been on the verge of joining Roma in July, with the Serie A club and his former side Bordeaux announcing an agreement had been reached.
But Barca came in at the 11th hour and secured a €41 million (£36.5m/$48m) deal for the talented winger, leaving Monchi incensed and the South American's agent claiming to have acted in "revenge" over a previous transfer.
Monchi subsequently gave Roma's in-house TV station a detailed outline of how the deal broke down, while he also vowed to sign a player "equal or even better than Malcom".
And in N'Zonzi – a €30m (£27m/$34m) addition from Monchi's former club Sevilla and member of France's World Cup-winning squad – he thinks he has succeeded.
"I said I would get a stronger player [than Malcom], but not necessarily in the same role," Monchi told reporters at a news conference on Thursday.
"Doesn't a world champion seem stronger than Malcom to you? For me Steven is better than Malcom.
"We already have stronger players on our team. We have improved the team without thinking about the defined roles.
"Malcom was a possibility because he seemed strong, but we went ahead looking for both the same and the other players.
"Ten days ago, it was impossible to sign Steven due to an economic reason, but thanks to the desire of his agent – who is his dad – to come here and the effort of the club, we succeeded. Nothing has changed. We have taken a strong player."
N'Zonzi had a difficult start at Sevilla after Monchi brought him to La Liga, but he went on to establish himself as one of the best midfielders in Spain and leaves the Ramon Sanchez Pizjuan as a World Cup winner.
But it was not success in Russia that prompted his desire to leave, with the Frenchman – who attempted to force a move in January after falling out with Sevilla's management – wanting a new challenge.
"No, it was not that [winning the World Cup]," N'Zonzi said. "I spent three wonderful years in Seville, but I felt the need for a new challenge and I chose a great club that will help me grow.
"Monchi helped me a great deal when I arrived at Sevilla. He's a top professional, who has shown he knows how to win. Now I just want to work hard and show everyone how good I am."