Federico Dimarco, on loan at Parma from Inter, scored a brilliant winner 11 minutes from time to earn his side a first victory back in Serie A at the expense of his parent club, although he could have earlier been punished for a handball on the goal line.
"It's a painful defeat," Spalletti told reporters. "When you find yourself with four points from four games in front of this crowd and considering the fixture list, it becomes difficult to find excuses.
"We did well for long spells, we were always in their half but we certainly need to offer more than what we did. The responsibility is mine above all if a lot of players are showing less than their full potential.
"I don't see this as a soft team. The guys are working in the right way with the attitude that you need. At times, perhaps we're creating more confusion by trying to change the things that aren't coming off.
"Up to their goal, we were in it but we wasted too many easy chances considering the quality that we have. We need to stay solid, keep our heads and learn also how to make the most of scrappy chances."
28 - 28 shots for Inter today: the last time the Nerazzurri had fired so many shots in a single Serie A match without scoring was back in February 2012 (30 vs Novara). Target.— OptaPaolo (@OptaPaolo) September 15, 2018
Replays appeared to indicate Dimarco's block on the line to keep out an Ivan Perisic shot was made with his arm and Spalletti's mood was darkened further after examining the footage.
"I have only seen the incident now but it's crushing, really crushing," Spalletti added. "Dimarco touches the ball with his hand, and it seems clear enough to me. There are no doubts in my mind, it is a penalty.
"However, I must think about improving the team and doing my job well because I have a strong squad here."
Inter's return to Europe's top table after six years away should have been a triumphant affair but Spalletti could be without defenders Sime Vrsaljko and Danilo D'Ambrosio for the Spurs game, while captain Mauro Icardi was only fit enough for the bench against Parma.
"Sime will not be available, while we will have to assess Danilo because he came off injured and could not recover," Spalletti said.