Grant's men dominated for an hour at Sukru Saracoglu Stadium but only had an own goal from Deivid as a reward before Colin Kazim-Richards came off the bench and levelled.
Deivid then grabbed the winner nine minutes from time, leaving Chelsea needing a win at Stamford Bridge next week to reach the semi-finals.
"I don't know what to say," Chelsea boss Grant said. "We played good football and deserved to be 3-0 or 4-0 up.
"One slip and they are back in the game.
"Normally it is a great result when you score away but because of our performance I'm very disappointed."
"We talked about it at half-time, about the chances we threw away," Grant said. "We needed to score more goals and didn't do it. This is football, one minute you are sleeping, then they equalise."
Ricardo Carvalho was guilty of a loss of concentration when former Bury, Brighton and Sheffield United forward Kazim-Richards raced through, but nobody was at fault when Deivid found the top corner from 25 yards.
"Now we play at home," Grant added. "We can win this game.
"Against Olympiacos (in the previous round) we didn't play well and got 0-0, here we played very well and lost 2-1. I don't know what is more disappointing.
"We played good football but football is a game of results. Now we go home one down but still there.
"It's part of life. We wanted to play the second game at home and now we have to use it.
"Of course we are unlucky but we are disappointed. We deserved to win, more than 1-0, and we lost."