Inter struggled to get a foothold in Wednesday's contest at Camp Nou despite Barca captain Lionel Messi's absence due to a fractured arm.
Rafinha, who was on loan at Inter last season, gave Barca a first-half lead and Jordi Alba wrapped it up for the hosts with seven minutes remaining.
And Spalletti was unhappy with the way his Inter team allowed Barca to set the game's tempo and rhythm, with Arthur giving a midfield masterclass.
"I’m sad mostly because I wanted a totally different approach in the first half," Spalletti told reporters.
"We were not brave enough to play the ball when we were in possession and we allowed Barcelona to play as they prefer.
"You cannot come here to defend and try to score on one counter-attack, you need to play better with the ball if you want to achieve something in this stadium.
"We didn't show as much character compared to our first two Champions League games. We weren't courageous enough and the opposition made the most of our attitude. We didn't do as much as we can.
"We also could have scored over the course of the game but they were stronger than us and deserved to win. They played well, passing the ball quickly and thinking fast."
Samir Handanovic made nine saves to keep the score down, while Philippe Coutinho hit the crossbar, but Barca moved three points clear at the top of Group B.
"Obviously we are happy about the result in the other game," Spalletti added. "But we must focus on the fact that we weren't at our best. We need to play much better next time because we are a team with ambition."