Juventus' lacklustre start to the season continued on Tuesday when they lost 2-0 to unfancied Maccabi Haifa in the UEFA Champions League.
With just two games in the group stage remaining, the Serie A side face an uphill task to advance as they are five points behind Paris Saint Germain and Benfica, who are locked on eight points apiece.
Juventus are also struggling to make much of an impact in Serie A with just three wins from nine games but Allegri is adamant it will not be the right decision to step down.
"I have never thought about resigning," Allegri said in an interview with Sky Sports.
"When a challenge becomes more difficult, it becomes even more beautiful. You have to come out with courage, desire and passion."
Chairman Andrea Agnelli said he felt ashamed of Juventus' performance in Israel and Allegri concurred with his boss' assertion.
"Agnelli is absolutely right," Allegri said. "It was one of the worst first halves we have done. It is not right to make a performance like that.
"We had the wrong attitude from the start. This match is difficult to explain, we just need to be silent.
"The performance was not up to par, especially from a character point of view. We just have to keep quiet, work and get out of this situation."
