Ibrahimovic hit his first United hat-trick to help the club put one foot in the last 16 of the competition prior to the second-leg trip to the Stade Geoffroy Guichard next week.
The 35-year-old now has 17 goals against Saint-Etienne throughout his career - more than he has managed against any other club - and he is hopeful of continuing his form in the coming weeks.
"We created good chances. It was important to get a good win at home and we bring it with us in the second leg. It was a good game but I think we can do better," he told reporters.
"Every time I've played against Saint-Etienne, with hard work there has been a couple of goals. I've scored a couple of goals tonight and hopefully I can do the same next week.
"We're winning but in a short time everything can change. It's important to keep getting the wins we need. Everything can change but we're happy at the moment. This is the decisive moment for the season. We are still in all four competitions. The fifth we already won (the Community Shield)."
Ibrahimovic has now scored 23 goals in 35 games for United across all competitions this season.