Steven Pressley has been promoted from his assistant's role to take over the reins but his first game in charge ended in defeat on Saturday with a 3-2 reverse at Hearts.
The loss leaves Falkirk four points adrift at the basement but Barr, who will join Hearts at the end of the season having signed a pre-contract agreement with the Tynecastle side, wants to prove that the side May has assembled is good enough to survive in the league.
He said: "I think we are still in a bit of shock with Eddie going.
"That's football and we wish Eddie all the best because he has done us a treat and we all feel partly responsible.
"It's not just his fault, it's our fault as well and we wish him all the best. He has been good for us, he brought through a lot of young boys and hopefully we can stay in this league and prove that to him.
"That's the main thing, it does not matter how we get the wins, they have to come sooner rather than later. We don't want to be cut adrift at the bottom, they have to come from somewhere."
Falkirk got off to the worst possible start when Lee Wallace's cross-shot from the left touchline caught goalkeeper Robert Olejnik off guard and flew into the net after five minutes.
However, the Bairns were level in first half injury time when Hearts defender Dawid Kucharski scored an own goal as he could not get out of the way of Marc Twaddle's cross.
Suso Santana drilled home the hosts' second in the 61st minute when he pounced on a loose ball in the box and Ian Black added a third with a 25-yard thunderbolt in the 67th minute.
Pedro Moutinho's 83rd-minute strike for Falkirk set up a tense finish but Hearts held on to claim their first win under recently-appointed manager Jim Jefferies.
Despite the result, Falkirk manager Pressley was pleased with his side's application and Scotland defender Barr reckons he can bring about a change in their fortunes.
He added: "Elvis has come in and is trying to put his messages across, he is doing well and I thought we showed that. It's a hard place to come with the crowd and I thought we were a bit unlucky.
"I thought we played some good stuff and maybe with a few of the goals, one was a bit lucky and one was an peach.
"I thought we showed good character and we were a bit unlucky, we could not get the goal at the end."
Source: Team Talk