Parma finished sixth in Serie A, one place and one point clear of Torino, and had looked set to compete in the continental competition.
After twice being refused the licence by Italy's Football Federation (FIGC), Parma appealed to the country's Olympic Committee's High Court of Justice, but that was rejected on Thursday.
Both sporting governing bodies made their decisions based on the club's financial irregularities.
"After our fantastic campaign, to have a chance to play in Europe represents an important achievement," Torino president Urbano Cairo said on the club's official website, www.torinofc.it.
"I am saddened for Parma. (Club president Tommaso) Ghirardi is a friend of mine and I can only imagine his bitterness.
"On the pitch, they finished one point above us and we congratulated them for that.
"However, in order to play in Europe you not only need a sporting result.
"With respect to us, I can only say that we are happy for our fans that had so much desire to see the team obtain this result.
"I'm happy for my team that played a great season, for our coach (Giampiero Ventura) and for all our club members.
"This is the icing on the cake."
Clubs must have a UEFA licence to compete in Europe.
Torino, UEFA Cup runners-up in the 1991-92 campaign, have not played in Europe since 2002, when they competed in the Intertoto Cup.