“It drives me crazy, with all the issues this country has that Salvini has time to chat about AC Milan,” said Gattuso.
Salvini, an AC Milan supporter, was in the stands at Rome's Stadio Olimpico during Sunday's game when Argentine Joaquin Correa snatched a last-gasp draw for Lazio.
Franck Kessie had put Milan ahead after 78 minutes.
“If I had been Gattuso I would have made some substitutions, the players were tired, I don't understand why he didn't change something in the second half,” Salvini told Italian television after the match.
“We had at least three who were exhausted with the heavy rain and the muddy pitch. Can someone explain this Gattuso stubbornness to me?
“When I saw a three-man defence today, I started praying.”
AC Milan are fifth in Serie A, one point behind Lazio, who occupy the final Champions League spot, and 15 points adrift of leaders Juventus.
Asked about Salvini's comments, Gattuso said: “I don't talk about politics because I don't understand anything.
“I tell him to think about politics because with all the problems we have in our country, if the deputy prime minister is talking about football, it means that we are in a bad way.”
- Five things we learned in Serie A
- Struggling Milan in 'World Cup final' against Inter
- Football: Struggling AC Milan sack coach Vincenzo Montella