Inter's 1-0 win over AS Roma in Wednesday's Cup showpiece was the first step of what could be an unprecedented Italian treble with the league title and Champions League final against Bayern Munich on May 22 also in Mourinho's sights.
Sneijder, due to be a key player for the Netherlands at the World Cup, limped off after five minutes with a perforated thigh muscle after the first robust challenge of a niggly match.
The influential playmaker could be out for several weeks, leaving Mourinho to mull his options with Inter two points clear of Roma in Serie A with two games left.
"Obviously I'm worried about Sneijder, we still have three games left to play and I don't know when he'll be back. It's a very difficult situation," Mourinho told a news conference.
The game, the fifth time the two sides had met in the Cup final in six years, was full of nasty fouls and minor brawls and finally boiled over late on when Roma captain Francesco Totti was sent off for an outrageous kick on Mario Balotelli.
"It's very hard for a final to be a great footballing spectacle and that's what we saw this evening, there was too much tension. What Totti did can happen, it's not my place to criticise but he lost his head," Mourinho added.
"I did not like how the game started. There was too much aggression, what happened to Sneijder was an obvious example."
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