Tigers' success in the Aviva Premiership clash at Sixways, secured through the help of two penalty tries, took them top of the league above long-time leaders Harlequins.
But Worcester's 11th yellow card of the Premiership season - two more than any other club - contributed heavily to their downfall.
Warriors' former Leicester fly-half Andy Goode was sin-binned just before half-time for dropping his knee on Tigers wing Scott Hamilton as the New Zealander scored a try.
With Goode still off the field, stand-in kicker Chris Pennell missed two penalty chances that Goode would probably have taken and possibly won the game.
"I can't wave a magic wand, unfortunately, and suddenly our penalty count goes below 10 a game and we get no yellow cards," Hill said.
"Over the next few weeks, it will be a process which we have got to keep going through.
"If we are still repeating the same offences in four to six weeks' time, then I have got to get the big stick out.
"We are being penalised, and we have just got to cut it out. It will be a hard-line approach to it. I've done the softly, softly.
"The crucial moment was the Andy Goode sin-binning. I am convinced if Andy had been on we'd have slotted those two penalties over. It was a key blow. Yet again, we found ourselves down to 14 men.
"It probably cost us the game - the small margins are crucial."
Warriors' first victory over the Tigers since March 2006 looked likely for large parts of a gripping encounter, but Leicester prevailed, courtesy of two second-half penalty tries, the second one being awarded in the final minute by referee JP Doyle.
Worcester wing David Lemi scored an early try and three Goode penalties ensured Warriors occupied the driving seat.
Leicester, though, mounted a fightback either side of Goode being sin-binned, with Hamilton touching down before Tigers claimed an opening penalty try that England international Toby Flood converted.
Flood also missed three penalties, but he added the extras to Tigers' late clincher on a night when Leicester welcomed back England flanker Tom Croft for his first appearance since suffering a neck injury last April.
Hill added: "I thought we played well enough to win. We played with a lot of ambition and kept the ball in hand.
"There were a few errors here and there, but our ambition was outstanding.
"I am bitterly, bitterly disappointed we lost the game, but if we continue playing like that - with that passion and quality - we are not going to lose too many more games this season."
Leicester rugby director Richard Cockerill admitted his team had to dig deep for their sixth successive victory in all competitions.
"Worcester played exceptionally well - we were outplayed in the first-half," he said.
"The try just before half-time really picked us up, but if Worcester had won tonight I don't think we could have had any complaints.
"We kept our composure after half-time, and luck was on our side in some ways. We needed to chase the game to try to win, and the effort from our lads to play for 80 minutes was massive.
"We didn't panic at half-time. We needed to have the ball and control it, and we knew we would get opportunities. It is a good win."
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