Milan Skriniar and Ivan Perisic struck the goals for Inter.
“It was not easy and our players were very professional, adapting to a style of game they were unaccustomed to," Spalletti told Mediaset Premium.
“It was very hot in Calabria, the pitch was very dry and slowed down the pace of the ball, while the wind also created problems in the first half.
“We were a little more fluid after the break, then Crotone tried to get it on second balls, flick-ons and Ante Budimir did a great job. Adapting to all of this is a sign of great quality.
“Handanovic did very well in goal, but we had an even clearer chance to score. Winning in these circumstances shows we are solid and can adapt."
This is the first time in his Serie A career that Spalletti has won the opening four games.
“We are not interested in the table right now, we just did what we had to do. It's a long road ahead of us and we won't get swept up in the moment. There are another 34 matches to go and we've got to win as many as possible,
“I think the team showed character, but we should've moved the ball around faster in the build-up play. Losing those balls cost us a few dangerous counter-attacks. Perhaps there wasn't much quality, but certainly character."