Inter's skipper had not scored for his club since November 3rd in a 1-0 win over Venezia.
But the Argentine got back on the scoresheet in the 71st minute on Saturday with a volley to put his team two up.
Inzaghi praised Martinez's resilience despite his recent struggles.
"Naturally, this situation was weighing on him, though we told him to relax and that he continued to give the team so much with his work. Lautaro (Martinez) will never be a problem for Inter, only a resource," Inzaghi told DAZN streaming service.
Alessandro Bastoni's header and Hakan Calhanoglu's penalty sealed Inter's fifth consecutive away win. Inzaghi praised his side's hard work from set-pieces and the contributions of players such as Federico Dimarco, Calhanoglu and Kristjan Asllani.
"At the end of the first half, we congratulated the team on their performance and knew we just had to keep going against a tenacious Cagliari side," Inzaghi added.
The manager was upbeat as he set his sights on Inter's fourth consecutive Supercoppa title and a 21st Scudetto after lifting the title last season.
"This exciting 2024 ends with the 20th Scudetto that will forever unite us with the fans and directors, but now we go to Saudi Arabia for the Supercoppa hoping to win it for the fourth year in a row."
Inter are level in the league on 40 points with Atalanta, who play at Lazio later on Saturday.
The two sides will also meet in the semi-finals of the Supercoppa Italiana in Saudi Arabia on Jan. 2, with the winner advancing to face either Juventus or Milan.
"We know that we are Inter, we have objectives and it is only right to declare them. It takes a lot of sacrifice, January and February will have us playing constantly, but I am fortunate to have players ready to give their all, whether for 95 minutes or five, and that is important," Inzaghi added.