The Nerazzurri boss admitted his side did not have it all their own way after booking their place in the semi-finals of the Coppa Italia
The Nerazzurri looked to be cruising into the semi-finals until two late strikes from Alessandro Diamanti and Manolo Gabbiadini sent the tie into extra time, before Andrea Ranocchia broke Rossoblu hearts with a last-gasp winner.
"The team dug deep again and showed their mettle," he told Rai Sports.
"We won it thanks to the strength of these lads. Inter kept plugging away out there and deserved to go through. We want to do well in this competition and we proved it tonight."
Stramaccioni also noted that the cream had risen to the top in the Coppa Italia and believes the semi-final line up reflects the best the country has to offer.
"We go into the semi-finals now and whether it's Fiorentina or Roma who qualify, along with Juventus, Lazio and ourselves, it's almost the same as the top of the league – like a final four in basketball."