Fernando Torres and John Terry scored in the second half at Stamford Bridge - Torres also missed a penalty when he hit the bar - after an equaliser just before half-time from Vlad Chiriches had cancelled out Juan Mata's opener.
At the break Chelsea trailed 2-1 in the tie, having been beaten in Romania, but they showed their qualities to eventually seal a place in tomorrow's quarter-final draw.
Cech said on ITV: "It's a big win because we wanted to qualify for the next round and I don't think this was the stage we wanted to go out of the competition.
"We made it hard for ourselves losing in Bucharest.
"When they made it 1-1 we knew we'd have to score twice but at the weekend we made up a two-goal deficit (against Manchester United in the FA Cup) at Old Trafford, so at half-time we knew we could score the goals."
Cech offered praise for Torres, adding: "He was working hard and took his chance great.
"It was a pity the penalty didn't go in for him but the important thing is we scored three goals so we are happy.
"We are in a stage where every game is like a final for us because we are chasing third spot in the Premier League and we are in the FA Cup and Europa League.
"It's not easy at times but we'll keep fighting."