The Reds host finals-bound Brisbane, four days after the club recorded its lowest-ever home attendance.
Just 3,539 spectators watched United's 3-3 draw with South Korean club Jeju United in their AFC Champions League fixture in Adelaide on Wednesday.
The record-low crowd comes amid Adelaide's horror A-League title defence - they've won only three of 22 games and are anchored in last spot.
Before the clash against the fourth-placed Roar, Elrich issued a rally call to Adelaide fans.
"Maybe a lot of people in Adelaide have given up on us," Elrich said.
"From what we have seen at the game midweek, 3,500 people is disappointing having such a small turnout when we're struggling out there on the pitch, and we know that in terms of results.
"But we need the support.
"It's all well good to be there for your friends and family when things are going well, but I'm sure they need you more than ever when things aren't going well.
"Us players, we know we're working as hard as we can to make things as good as can be on the pitch.
"But everyone else has got to chip in and do their bit as well."
Elrich conceded some of his Adelaide teammates were "playing for their futures" against Brisbane.
"We need a win. It's not so much looking to make the finals. It's more for some pride, personal pride and the team, club," he said.
"Where we are in the table is not where Adelaide deserve to be ... we just need to win this game, get a bit of confidence in the team, and then we build on that."
STATS THAT MATTER
* Brisbane have won only one of their past four games against Adelaide, with a 4-0 result the most recent match.
* The Roar are unbeaten in their past four away games (two wins, two draws).
* Adelaide have won 52.4 per cent of duels contested this season, second-most of any team in the competition behind Perth Glory (53.3 per cent).