Winger Eden Hazard curled an 85th-minute free-kick over the Liverpool defence and past a static Jose Reina inside the far post just when it seemed the visitors had weathered the storm. But it could have been far worse had substitute Pierre-Emerick Aubameyang’s shot not hit the post and gone wide late on.
Benitez had called for his players to show Monday’s defeat to Wigan had been an aberration and he felt they had done that.
“It was an improvement from the last game. The players’ reaction has been very positive,” said the Spaniard.
“I am disappointed with the result but really pleased with the effort of the players. They were fantastic today.
“It was against a good team on a difficult pitch. The reaction has been good.
“I think Lille started really well. We knew they had pace – you can watch videos but until you see them on the pitch you don’t see the pace they have.
“It was difficult to stop them but little by little we had more control.
“When we had that control and were going forward we conceded the goal.”
Despite conceding plenty of possession to their opponents Liverpool could easily have been 2-0 up at half-time had Ryan Babel not shot too close to goalkeeper Mickael Landreau, who also brilliantly saved Fernando Torres’ close-range header.
Benitez admitted that those missed opportunities cost them and could have put a completely different perspective on the match.
“When you play away you have to score when you have chances. To score an early goal you can manage the game but we worked hard today.
“To have two or three chances to score and then concede a (goal to a) free-kick... we have to be positive.
“It is clear, particularly in this competition, you have to score away because it is an advantage.
“We were just not strong enough today but there is still 90 minutes to play. I am confident we can beat anyone at Anfield on our day with the fans behind us.
“In every top side, especially when you are not having a good season, every game is important.
“We have to be ready for Monday’s Premier League match against Portsmouth and to win and then be ready for 90 minutes in the Europa League.” Lille coach Rudi Garcia felt his side were worthy winners.
“In European competitions winning 1-0 is always a good result,” he said.
“But Liverpool still managed to create some opportunities and we had a goalkeeper who made two or three really great saves.
“I think we deserved to win tonight. I am satisfied with what we showed and we will do everything we can to qualify. To beat Liverpool, who were the favourites when the draw was made, is good.
“But we will need to score in the second leg, we can’t go there and play for a 0-0.”
LILLE: Landreau, Emerson, Beria, Rami, Balmont, Cabaye (Dumont 73), Obraniak (Toure 83),Chedjou, Mavuba, Hazard, Frau (Aubameyang, 77)
LIVERPOOL: Reina, Johnson, Agger, Insua, Carragher, Gerrard, Babel (Riera 73), Mascherano, Lucas, Torres, Kuyt (El Zhar 88).
Referee: A Larsen (Denmark).