The hosts entered the match with a solitary win to their name in Serie A this season but will rue not doubling that tally after a VAR review denied Camillo Ciano the breakthrough.
Samu Castillejo twice went close before then but, not for the first-time this season, a talented Rossoneri attack lacked cohesion and incision.
Milan last found the net on December 2 and they remain outside the Champions League places on goal difference – the job of remedying that situation might soon be taken out of Gattuso's hands.
The 40-year-old wore the anguish of a man under pressure in the third minute when Patrick Cutrone botched a close-range opportunity.
Castillejo, operating on the right wing, provided Milan's main first-half threat – pulling a shot against the base of the post before cutting inside again and forcing goalkeeper Marco Sportiello to push clear.
Frosinone grew into the contest and, after Gianluigi Donnarumma made a sharp save from marauding wing-back Paolo Ghiglione and Andrea Beghetto blazed over, VAR came to Milan's aid.
Ciano crowned a sweeping counter-attack but Lorenzo Crisetig was belatedly adjudged to have fouled Hakan Calhanoglu when he turned over possession.
Milan resumed on the front foot, although Andrea Pinamonti was agonisingly close to turning in another teasing Ghiglione cross before the hour.
Ricardo Rodriguez fizzed a speculative long-ranger wide in the 67th minute, while Ghiglione sent Donnarumma tumbling to his left to push a shot behind.
Gattuso could have done without an out-of-sorts Gonzalo Higuain twice hacking over from inside the box late on. Donnarumma then spared Gattuso and Higuain's blushes with another superb stop from Ciano in stoppage time.
What does it mean? Gattuso sackwatch more interesting than his team
Milan could end Boxing Day down in eighth position and, if it was not for Gattuso's status as a club icon, he might well have been put out of his misery before now. The presence of former Arsenal chief executive Ivan Gazidis at San Siro and resultant links with Arsene Wenger might be easy dots to join but it does not make life any easier for Gattuso, who needs to call on every ounce of his old on-field combativeness to turn this around.
Ghiglione dances into Serie A spotlight
Signed on loan from Genoa for this season, Ghiglione was restricted to three substitute appearances under Moreno Longo this season but successor Marco Baroni – still unbeaten after back-to-back draws in his first two games at the helm – threw him a starting berth. It is one he is likely to keep after being Frosinone's driving force here, helping to overturn first-half pressure and attacking with vigour down the right flank. But for Donnarumma, he might have been the matchwinner.
Higuain toiling without reward
Milan's goal drought has much to do with the fact one of the most reliable goalscorers in Serie A over recent years has not found the net since October 28. Higuain bore all the hallmarks of a striker grasping for form – gamely running the channels, straining for something to happen and generally absent when half-chances dropped in the box. The Argentina striker has been linked to Chelsea and his late misses suggested a chance of scenery would do him no harm.
Key Opta Facts:
- AC Milan have played four Serie A games in a row without scoring for the first time since December 1984.
- The last AC Milan goal in the first half of a Serie A match was in October versus Genoa.
- Milan are the only Serie A team without a goal in the last four league matchdays.
- Milan have won only five of their last Serie A games played in December (D11, 6L)
- Milan fired 25 shots today, more than in their any other Serie A 2018/19 game away from home.
- Gonzalo Higuain has not found the net for nine games in a row (802 minutes in all comps).
- Milan collected three clean sheets in the last four Serie A matches, the same they had in the previous 25 league games.
1984 - AC Milan have played 4 Serie A games in a row without scoring for the first time since December 1984. Dark. #FrosinoneMilan— OptaPaolo (@OptaPaolo) December 26, 2018