Real suffered a shock 4-1 defeat at Santiago Bernabeu to give the Eredivisie side a 5-3 aggregate victory after Santiago Solari's side had taken a 2-1 lead into the second leg.
Solari's job is now under extreme scrutiny following three defeats in seven days. The former Castilla boss only replaced Julen Lopitagui four months ago, who himself only took up the position last summer following Zidane's departure.
And Gullit believes Zidane's timing was impeccable: "Zidane was clever enough to get out of there on time when they lost Ronaldo," he said while appearing as a pundit on beIN Sports . "That's the whole point. And whoever comes after that has a difficult task.
"You have no Ronaldo. That's 50 goals you don't have."
Although Solari is contracted to Real until 2021, his position is becoming almost untenable after Dani Carvajal bluntly stated the European champions have had a " sh*t season".
World Cup winner Marcel Desailly was damning of the Argentine's influence during his tenure: "He [Solari] has not brought any kind of new philosophy, new tactical set-up. He should have not been scared. He has not changed anything on the set-up.
"You either reinforce your defensive block, or you create and you allow one of them to express themself in a better way. He has not done it. It's the same shape, same movement. So we have to blame him."
The defeat comes three days after Real suffered a Clasico defeat to Barcelona, giving a 12-point advantage to the Liga leaders, and nearly a week after they were knocked out of the Copa del Rey semi-finals by Ernesto Valverde's side.
After those defeats, Gullit said he was not shocked by Real's Champions League exit.
The former Chelsea boss continued: "It was not a surprise. Because seeing Madrid lately, seeing the first match they [Ajax] played at home - and they didn't deserve to lose - I saw opportunities, especially in Madrid.
"Then you see the game Barcelona at Madrid, played them [Real] off the park as well. You see the midfield and you think to yourself, 'Oh my God. That is exactly the team they want to face!'
"And the worst part is this has been the easiest game of the season. That is even worse. Against Madrid! Not even in their home competition do they have easy games like this."