The win took Liverpool to 80 points and also guaranteed them a top-three place in the league and a spot in next season's Champions League.
Aspinall's son James was one of the 96 Liverpool supporters who died in the tragedy in 1989 and she spoke during a memorial service at Anfield on Tuesday to mark the 25th anniversary of the disaster.
"We had the memorial service this week and that was really touching," Rodgers was quoted as saying by the British media on Monday. "So I decided to use words of Margaret Aspinall. We put them up on the wall.
"She talked about stress and how it can prove difficult for you but can also offer great determination to fight.
"Those were the words that we gave the players before the game. This is really one club at this moment and we will all fight to achieve the ultimate goal."
Liverpool needed all their determination to ensure they walked off the field with all three points against their resilient opponents in a tense finish.
The Merseyside club started quickly and were 2-0 up but first Gary Hooper pulled a goal back to make it 2-1 and after Raheem Sterling's second, Robert Snodgrass nodded in to make it 3-2.
Liverpool are now five points ahead of Chelsea (75), who suffered a shock 2-1 defeat by bottom-placed Sunderland on Saturday, while third-placed Manchester City are on 71 with two matches to spare.
- Sports & Recreation