"I am happy, because we won a cup that we wanted, to confirm what we did last season. Fiorentina are a quality team who caused us a lot of problems."
Inter grabbed two early goals through Edin Dzeko and Henrikh Mkhitaryan and will take a big advantage into the second leg back at the San Siro on Tuesday.
It will be Inter's first semi-final appearance since they won the European Cup for the third time in 2010, the last Italian Champions League triumph with Juventus losing the 2015 and 2017 finals.
Spezia struck through Daniel Maldini and M'Bala Nzola's penalty to beat Inter for the first time, with Romelu Lukaku's equaliser from the spot counting for nothing in the end.
Porto midfielder Otavio was sent off 12 minutes from time and Belgian striker Lukaku took full advantage to boost Inter's bid to qualify for the quarter-finals of Europe's premier club competition for the first time in 12 years.
The annual meeting between the Coppa Italia winners and Serie A champions was played at the King Fahd International Stadium in Riyadh, Saudi Arabia.
Napoli are still top of the table with 41 points after 16 games but their advantage over second-placed AC Milan, who beat Salernitana 2-1, narrowed to five points.
Lazio provisionally lead the standings with seven points from three games, while Inter are a point behind in fourth.
Needing four points from their final two games of the season, Milan stand on the brink of a first Serie A title since 2011.
Inter struggled considerably in the first half against an Empoli side who have won just once in their last 20 games.
Chasing a first league crown since the days of Diego Maradona, a sold-out stadium which bears their hero's name will host two teams locked on 57 points.
AC Milan slipped up for the second time in as many weeks on Friday with a 1-1 draw with Udinese which gave their Serie A title rivals a chance to reach them at the summit.
Lukaku's comments about being dissatisfied with life at the club are unhelpful, manager Thomas Tuchel said on Friday.
The champions are on an unstoppable run of league form, winning their last five games without conceding a goal and going ten matches without defeat.
Simone Inzaghi’s side are third with 24 points, four behind leaders Napoli and second-placed AC Milan, who face Salernitana and AS Roma respectively later on Sunday.
Inzaghi takes defending Serie A champions Inter Milan to former club Lazio this weekend.
Dumfries isn't worried about living up to departed star Achraf Hakimi as the Netherlands right-back eases into life at Inter Milan.
Romelu Lukaku said he will remain at Inter Milan next season after the Belgium forward helped them to their first Serie A title in 11 years.
Conte's Inter travel south to basement club Crotone on Saturday where a win would allow them to put one hand on a trophy they last won in 2010.
Hakimi came off the bench and minutes later set up Italy defender Darmian to grab the winner in the San Siro.