The first half ended level after goals from Diomansy Kamara and Marc-Antoine Fortune had been cancelled out by Michael Paton and Darren Mackie.
The Parkhead side went two clear with goals from Robbie Keane and Aiden McGeady - but MacLean reduced the deficit from the spot before grabbing a dramatic late equaliser as Celtic defender Darren O'Dea was sent off in the dying stages.
MacLean told ESPN: I spoke to the manager (Mark McGee) who sold the club to me and you can't buy days like this. I'm glad I came now.
"We knocked the ball about well today.and luckily enough showed enough fighting spirit to come from a goal down twice and two at the end."
Mackie added: "The fans were right behind us - unfortunately we didn't get the win but to fight back from two down is good.
"It was a good show again, the start was really quiet then it was goals, goals, goals."
McGhee added on ESPN: "I think defensively we could have done a little bit better. Maybe the game was there for us to win today but there were a lot of positives nonetheless.
"At 4-2 we still felt we could get something. I did - and not in a dreamy sort of way. I wasn't surprised when the fourth goal went in.
"We made a shocking start.you feel you have to get the first goal against the Old Firm. We were always playing catch-up."
McGhee acknowledged he has reasons to be cheerful, adding on ESPN: "We've got Sone (Aluko) and Zander (Diamond) back now so our squad is as strong as we've had at any point in the season.
"We've let ourselves down recently after good performances but now we've drawn with Hibernian and Celtic and scored six goals, which is an improvement on our ratio for the season - although we've not won either game."
Celtic boss Tony Mowbray looked deflated but said: "I'm stunned - I really thought the game was finished at 4-2 but we inexplicably gave them a lifeline, they grabbed it late on and it's a frustrating day for us."
The former centre-half acknowledged: "They pushed very hard for the equaliser and ultimately got it but we talked before the game about our defensive problems and we didn't stand up to what came our way today.
"We scored some great goals but lost poor goals to set-plays and sometimes you need someone to go and head the ball.Aberdeen don't have huge height in their side."
Mowbray defended the substitution of Robbie Keane, who was taken off shortly after Aiden McGeady had given the visitors at 4-2 lead at Pittodrie.
The Celtic boss continued on ESPN: "He's not a giant, he doesn't stand and head corners away for us.
"Georgios Samaras does - he's 6ft 3in - and that was part of the thinking. I don't think it had any relevance in the game."
The result will please Old Firm rivals Rangers, who take on Hibernian at Ibrox on Sunday.
But Mowbray added: "It's a point for us. I don't know what the results will be later, or tomorrow. It might be a point gained, we'll wait and see."