Inzaghi came into the Serie A meeting at San Siro under pressure, with rumours beginning to circulate that assistant Mauro Tassotti could soon be replacing him at the helm.
It looked as though Inzaghi would earn a reprieve when Milan led 2-1 with just a minute of stoppage time remaining, but Lopez struck to earn Verona a draw and pile further misery on the coach.
"That [being fired] is not a question for me," he told Sky Sport Italia.
"I go forward with my head held high, because I give my all and so does the team.
"We have few alternatives, there's no point hiding it. I knew this was a complicated match, we should have done better throughout the 90 minutes, but if we had won it would have been important as a morale-booster.
"Everyone has their opinion. I think I know when to use the carrot and the stick. We might have played badly tonight, but nobody can say the players didn't put in the effort.
"In training I saw their hunger, the work and the spirit. We do need to play better, we drew and I have to look forward.
"I don't like trials by media, I know you will hold one anyway, but I have to focus on my team.
"Obviously the team were very disappointed, but this is football - those who score at the last second celebrate, those who concede will have difficult days.
"We still have 12 games and have to bring the games home, that's what we did not do tonight."
