Inter coach Roberto Mancini bemoaned his side's poor finishing and conceded it is now difficult to qualify for the Champions League following the 1-0 defeat to Genoa.
Genoa captain Sebastian De Maio scored the only goal of the game in the second half after Inter had spurned several clear-cut opportunities to break the deadlock.
Inter are seven points from third spot and the last remaining Champions League slot in Serie A with four games left after Roma came from behind to beat Torino 3-2.
"The team produced a great performance and we definitely should have won. We had so many chances that we deserved to be 2-0 up by the end of the first half," Mancini told Mediaset Premium.
"Unfortunately we couldn't finish on a number of occasions and then we went to sleep for their goal, as has happened several times this season. It was a crazy match.
"It's never an easy match here. Last season we conceded in the 93rd minute and that was harder on us than we deserved."
Inter visit Udinese on Saturday and Mancini knows it will be an uphill battle to finish third.
He said: "It was very difficult before and it's very difficult now. As I've said, we need to work hard because we're struggling to score and we're not able to score the goals we deserve."