The once great French club have hit form recently after returning to Ligue 1 earlier this year for the first time since 2009.
Nantes win away to Bordeaux on Sunday has helped prove they are a serious contender in Ligue 1 this season but Der Zarkarian was careful not to get too carried away after the victory.
"Beating a Bordeaux side that hadn't lost in seven league games is good," he said.
"They had no luck, we did. My players were strong in defence and always carried a threat."
Nantes have been crowned champions of France eight times and were a powerhouse club from 1965-1983 when they won six league titles.
The east French club last won Ligue 1 in the 2000/01 season but have struggled since with two separate stints in the second tier.
Nantes' recent form has been helped by Serbia international Filip Djordjevic, who has scored eight goals for the club, making him one of the highest scorers in the league so far this season.
Djordjevic is only one goal behind Monaco's Radamel Falcao and Paris Saint-Germain's Edinson Cavani but he too is cautious about Nantes' recent form.
"I am having a lucky spell and making the most of my chances," Djordjevic said.
"Now we'll have some time to recover as there is an international break coming up, then we have Monaco at home next.
"We'll try to leapfrog them into third place."
Der Zarkarian meanwhile is more focused on retaining their spot in Ligue 1.
"The aim is to pocket 42 points (the usual total required to secure Ligue 1 safety) as soon as possible," the 50-year-old coach said.
"When that is done, we'll see what we can do next. The aim is to stay in Ligue 1."
