"I spent nine wonderful years at his side," Moreno told reporters in Monaco late on Monday.
"I only have thanks. What happened a few weeks ago is already in the past," he added.
Moreno, 42, was part of Luis Enrique's staff at Roma, Celta Vigo and Barcelona before following him to the Spanish national team, reports Efe news.
When Luis Enrique took a leave of absence in June to care for his ailing daughter, who died two months later of cancer, Moreno took charge of La Roja. In November, Enrique returned to the head coaching position under a previous agreement with the Spanish football federation and declined to reappoint Moreno as his assistant, calling him "disloyal."
"I have been a coach for 28 years. Since I was 14, I have been training and now the important thing is this presentation. The past is there, but you have to leave it behind," Moreno said.
He said that while he received many job offers after leaving the Spanish national team, only Monaco made him feel that he was their first choice.
"If one wants to be a high-level coach, one needs a project of magnitude," the Spaniard said.
Moreno, accompanied by club vice president Oleg Petrov, said his ambition is to make Monaco a team able to "control the game" in the manner of Ligue 1 leaders Paris Saint-Germain.
"Systems are not what's really important, what's important for me is style," he said, adding that he is ready to adapt his formation to the individual qualities of the players.
In a similar vein, Moreno declined to be drawn on what, if any, acquisitions Monaco will be looking to make during the winter transfer window.
"I will not make it public - that would be disrespectful to my players," he said. "Monaco have a large squad but we have to be attentive to the market to find good players. But I am not going to highlight particular positions in public."
Monaco are currently seventh in Ligue 1, trailing 17 points behind PSG.
( With inputs from IANS )