The tie at the Turk Telekom Arena started on Tuesday, but play was called off due to a blizzard and restarted the following day, 31 minutes into the match with the score at 0-0.
Conditions worsened considerably as the game went on, but Wesley Sneijder pounced in the 85th minute to send Galatasaray through, making them the first Turkish club to reach the Champions League knockout stages in consecutive seasons.
However, rather than revel in the victory, Mancini agreed with Juve counterpart Antonio Conte that the pitch was not safe to be played on - although he hinted that the Serie A champions had been happy to get under way before the game's resumption.
"It was difficult to play football in these circumstances and I said beforehand it was dangerous for the players, so perhaps better not to play," Mancini told Sky Sport Italia.
"Last night (Tuesday) was practically impossible, as a sheet of ice had formed over the pitch and nobody wanted to continue. I told the UEFA delegate that in my view it wasn't right to play today either.
"At half-time it was already too late. Juve wanted to play before the game, or at least they didn't say anything. I agree with Conte, it was impossible to play football for either side. It became a lottery.
"After that it was an open game and we were more aggressive, so deserved the victory, perhaps because we knew that we had to win."
Mancini's first game in charge of Gala was October's 2-2 draw at the Juventus Stadium.
He believes his side have shown improvement since and deserved to go through.
"It was a difficult situation when I took over, as we’d lost our first home game 6-1," he added.
"We were good and lucky to get a point in Turin, then deserved to win this match."
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