Mauro Icardi got both Inter goals, the second coming in the 79th minute, shortly after an equaliser from Alberto Paloschi.
Inter’s midweek win against PSV Eindhoven in the Champions League was a fifth in succession and they stretched that run on a night where they had to graft for reward.
Mirco Antenucci missed a penalty for SPAL, and Spalletti recognised his team had been in a battle.
He told Sky Sport Italia: “It wasn’t an easy game in a lot of regards and the guys managed it well, fighting hard and showing strength. At times, we gave the ball away too much which allowed SPAL to force things, this is what we need to improve on.”
He added, according to Inter’s website: “The team showed character against a side that had a lot of intensity.
“The reaction after their equaliser was immediate, we went to go and get the three points and this is a characteristic that few sides have. We need to keep this because it’s really important.”
Match-winner Icardi, who was expertly teed up for his decisive strike by Ivan Perisic, compared the fixture to last season’s corresponding game, which finished in a 1-1 draw.
The Argentinian striker said: “We knew that it wouldn’t be an easy match, just like it wasn’t last year. We were aware that we would have to do more and the main thing is that the team won.”