The Lions failed to make their numerical advantage count at the King Power Stadium following Wes Morgan's third-minute dismissal until Alan Dunne popped up in the 87th minute for his first goal in three years.
The win takes Millwall to 50 points - usually considered enough to avoid relegation - but Jackett believes there is still work to be done in the Championship
"I think it's going to take more than 50 points," said Jackett, whose side have now gone six and a half hours without conceding a goal.
"We're 50 points with nine games to go and we'd rather get safe sooner rather than later.
"I've thought for a little while that 50 points won't be enough to keep you up. It does look like every club at the bottom is going to fight to the end. Fifty points is something that you look for but we're on 50 points with nine games to go so if we finished on that I'd be very disappointed."
Jackett admitted his side had struggled to break down the Foxes.
"We started brightly and I don't know if we surprised Leicester in that but we should have been a couple of goals ahead by half-time," he added.
"Not taking those opportunities looked like it was going to cost us and it did seem as if the game was petering out into a nil-nil draw.
"I'm very pleased for Alan Dunne, who's come back into the side in recent weeks and done very well for us defensively, but to pop up and finish with such composure showed terrific quality.
"I think his last one at Walsall was a cracker as well so when he does score their good ones and to get the winner today is a crucial one."