Having lost to Stoke and Tottenham, the Reds laid the foundation for their 2-1 win over Mick McCarthy's side with a morale-boosting midweek Carling Cup win over Brighton.
However, that would have counted for nothing had they not picked up three points at Anfield, especially with tough matches at Everton and home to Manchester United to follow.
"It was an important win, especially after the defeat against Spurs," said the Brazil international.
"It was a heavy defeat at Spurs (4-0 - in which they had two men sent off) and it was important to win in the Carling Cup and get three points in the Premier League which gives us chance to be close to the top four.
"Of course against Spurs everyone could see the situation of the game when we lost two men and it is always difficult to come back.
"Against Stoke we didn't deserve to lose because we played very good football but when you have two defeats in a row the confidence gets low.
"We spoke before the game against Brighton that we needed to win, get back on track and go into the next round and come into this game with confidence and win and that is what happened."
Kenny Dalglish's side, which showed only one change from that which lined up at White Hart Lane with Martin Kelly replacing the injured Daniel Agger, appeared to show no after-effects of their mauling the previous weekend.
Charlie Adam's long-range shot was diverted in by a diving Roger Johnson and Luis Suarez did what he has done since arriving in January from Ajax by mesmerising defenders before beating goalkeeper Wayne Hennessey at his near post to put them well ahead at half-time.
But such is Liverpool's woeful defensive record, with just one clean sheet in eight matches now, it seemed almost inevitable they would put themselves under pressure at some point.
That it took less then five minutes of the second half for interval substitute Steven Fletcher to power past Jose Reina was surprising.
Even then the hosts had chances to put the result beyond doubt with Suarez forcing a point-blank save from Hennessey, Andy Carroll heading against a post and Stewart Downing shooting too close to the Wolves goalkeeper on a counter-attack.
"It was a tough game and we had plenty of chances but only took two," added Lucas.
"It is hard when you concede a goal early in the second half. We tried to control the game and I think we managed well.
"I think sometimes we are a bit unlucky; we twice hit the post and there were a couple of saves by the keeper but that means we are creating so we just have to finish better.
"If we can score more goals it will be good but it was an important win because we had defeat at Spurs."
Carroll's role in the team has been the subject of endless debate but this was definitely his most complete contribution, albeit without a goal, this season.
The fact it was his second successive full 90 minutes may just be coincidence but the £35million club-record signing is at least starting to show he can play alongside Suarez.
"Andy's performance had everything except a goal," said Dalglish.
"We could not get more out of the big fella and we were delighted with him and for him.
"I don't think Andy played too many times with Luis last season because he was injured but the two of them played well."
It was a third successive defeat for Wolves, who have now taken one point from four matches, but McCarthy had reasons to be positive.
"I've said before we don't want to be a team of heroic failures playing well and not getting anything," he said.
"While it wasn't the result we wanted it was a far better performance.
"I thought the lads were terrific and it was more like a Wolves performance - more like that and we will pick up points."