Ausilio spoke to the press following the UEFA Europa League Group F encounter as coach Roberto Mancini, who is 50 today, was serving a European ban from his time in charge of Galatasaray.
Already trailing to Ruslan Rotan's volley, Handanovic kept the scores level with a penalty save from Yevhen Konoplyanka - his fourth of the season for the Serie A side, who went on to seal qualification for the round of 32 in first place.
Zdravko Kuzmanovic equalised after half an hour before Inter's task was made harder within a minute of the restart when Andrea Ranocchia received a second booking.
But Pablo Daniel Osvaldo popped up four minutes later to slot home and, despite late Dnipro pressure, Inter held on to secure the three points.
And Ausilio lauded Handanovic's 'remarkable statistics' after his sixth consecutive penalty save gave Inter the impetus to go on and win.
He told Sky Sport Italia: "It would be better not to concede so many penalties, but with a goalkeeper like him we seem to have the advantage. His statistics are remarkable and there's nothing casual about it. He is a professional who works hard for these results."
Even though the hosts did not play well and rode their luck at times, Ausilio was only concerned with the result, which takes their unbeaten European run at the San Siro to 10 games.
"It was important to win today, we knew it would be tough with 10 men, but we booked our spot in the next round and that is what counts," he added.