Speaking after his team drew 1-1 with Genoa to make it five games without a win in Serie A, Allegri argued Milan were 'absolutely dominant' and deserved a victory at the San Siro.
Mario Balotelli had a penalty saved eight minutes before half-time - just the second time in his career that the Milan striker has failed to convert from the spot - and Allegri bemoaned his team's inability to convert their chances.
But when challenged after the match about what he should do next, Allegri denied he was about to give up.
"I have not run out of words and ideas, otherwise I'd have already left. Tomorrow we will meet up and start preparing for the Champions League," the 46-year-old told Sky Sport Italia.
"We drew an incredible game and it was the same against Chievo (two weeks ago), where we dominate and can't seem to get the victory.
"When the team plays at this level, all we can do is be more determined and accurate in front of goal.
"If the team was lacking organisation or didn't know what it should be doing, it wouldn't have put in a performance like this tonight. We were absolutely dominant."
The draw left Milan in 11th in Serie A, 10 points adrift of the Europa League positions and Allegri conceded his - and the club's - frustration at their predicament.
"It's only natural there is bitterness that we are without a win in a month," Allegri said.
"In terms of performance we did much better tonight and conceded practically no chances. Of course now we have to work even harder and do even better, as what we’re doing is not enough.
"It is strange to see the table, especially as we deserved more but if we are there then it means we haven't done enough. We all have the determination to improve and climb the standings."
Genoa's head coach Gian Piero Gasperini was thrilled with his team's ability to grind out a draw after they lost Thomas Manfredini to a red card after the 33-year-old defender conceded the penalty, which Mattia Perin saved from Balotelli.
The draw extended Genoa's undefeated streak to four games.
"It is undoubtedly a point worth its weight in gold," Gasperini said.
"We had to defend for most of the game, as is natural when going down to 10 men before half-time and unfortunately the match lost its spectacle too.
"It's an important result, one earned above all with pride and determination."
