The 21-year-old forward teamed up with the St Mary's Stadium outfit from Belgian side Standard Liege on a four-year contract in June.
The Mali international made his debut appearance against the Reds, replacing Ryan Bertrand in the 77th minute of the encounter.
Hasenhuttl, who rued his side’s failure to earn a positive result against Jurgen Klopp’s men, is pleased with the cameo appearance from the winger.
“To win against such a team you need to have a perfect game and we didn't quite have that,” Hasenhuttl told the club website.
“Bringing Moussa on was an offensive substitution. We tried to bring him into the game and force 1v1 situations and he had a few good ones.
“One situation was the moment where we created a chance. It's good for him to come in and to be able to show strength the first time.”
Djenepo will hope to start when Southampton take on Brighton and Hove Albion on Saturday, August 24.