The Dons could relegate the administration-hit Gorgie side with a victory at Tynecastle on Wednesday night.
Gary Locke's men staved off demotion with an incredible Edinburgh derby win over bitter rivals Hibernian on Sunday but face a tougher task as they host the League Cup winners.
Even if they do muster their third win over the Pittodrie men, they would still be left with a massive 16-point gap separating them from second-bottom St Mirren, with just 18 to play for.
With demotion looking inevitable, McInnes lamented the potential loss of one of Scotland's most decorated clubs from the top flight.
He told RedTV: "It would be a shame to lose them from the league. They are a proper club who unfortunately have not been run properly. They will be a miss to the league.
"Gary Locke deserves a lot of credit. He has been a steady influence. He is a good person."
Despite their wretched season, the Jambos have enjoyed some of their best moments against Aberdeen.
They beat the Reds 2-1 at home back in August before claiming a 3-1 success in the Granite City two-and-a-half months later.
But defender Mark Reynolds does not expect an easier ride even though Hearts are on the brink of going down.
"We know it's going to be tough and we know Hearts are fighting for their lives," he said. "They are going to be dangerous - they've proved they can take points off us this season. We go there expecting a hard game but looking to come away with three points.
"Hearts have shown in previous games that regardless of what's happening off the pitch it's something they can't influence so they try and do the best they can and try and pick up the points like every other team."
Hearts' relegation woes aside, Aberdeen have their own cause to concentrate on as they look to beat Motherwell to second spot.
They have a two-point lead over the Fir Park outfit but McInnes does not want his side slacking off.
He said: "As with any game we set out to win it. It will be a very competitive game. We have a lot of work to do to get a result. Hearts will be on a high after beating Hibs on Sunday. The atmosphere created on Sunday by the Hearts fans was very good.
"We have still got it all to do if we are to finish in one of the European spots. We have to keep showing the same commitment that we have shown all season."