The Premier League leaders got off to a perfect start when Kris Commons fired them ahead with around 12 seconds or so gone.
However, in similar fashion to last week's 3-2 defeat at Ross County when they surrendered a two-goal lead, Celtic threw their initial advantage away.
Dons striker Scott Vernon levelled with a minute of the first half remaining after Hoops defender Kelvin Wilson was robbed in the box by Josh Magennis, who then grabbed a double for himself after the break with the home defence in some disarray.
The champions rolled up their sleeves though, and Charlie Mulgrew reduced the deficit before Gary Hooper levelled with three minute remaining, leaving Samaras, who had replaced Beram Kayal, to hook in a marvellous winner with seconds left of added time.
While Celtic are 15 points clear of Motherwell at the top of the table after the 4-3 win, Lennon is aware that his side have lost 29 goals in 31 SPL matches this season.
"I expect the quality players we have to eradicate those mistakes quickly," he said.
"We can't keep conceding goals and expect us to go and score three and four at the other end.
"So, considering the last two seasons defensively in the league when we were very good - I think we lost 21 and 22 goals - we are not as good this season.
"Maybe that's because we have lost some experienced centre-halves in (Glenn) Loovens and (Daniel) Majstorovic, but it is an area that we will look to improve on between now and the end of the season.
"I don't detect a lack of confidence but they are not playing to the levels that they can do.
"I don't know the reasons why, just a few of them are off colour.
"We gave a goal away that sometimes you can't legislate for and I thought the second goal was poor as well, we should have done better with that.
"The third goal was a great shot and a deflection so you can't do anything about that, so what you want is to see if you can dig yourselves out of it and some players dug some other players out.
"But to be fair, over the course of the season, those players who were maybe a little bit off colour yesterday have been fantastic for us."
Magennis was moved from defence into his preferred attacking role by Aberdeen boss Craig Brown, and he put in an impressive performance.
"I think I did all right at right-back, it just depends where the gaffer wants me," Magennis said.
"Hopefully after yesterday he will have faith in me and play me up front more often."