Attacker Rabbi Matondo also had a super impact when he came on, with the boss thrilled with the way his side ended the match, running out 4-0 victors.
"It's the impact I want from the squad,” Beale told RangersTV. “We are trying to run and press and harass teams, so naturally, people if they leave it all out there are going to get tired.
"It is important the guys come off the bench with a real desire to show what they can bring to the team and as Livingston got tired today, they had to face Sima and Matondo, and Kieran Dowell coming on. That was really important as well to the game.
“I have to say as well, the fans today at the start of the game, they have had a tough week but they really got behind the team and Kieran Dowell's goal probably at the end is a reward for all the support they have given the group this week as well."
The manager also cast an eye ahead to Tuesday’s Champions League qualifier second leg, with Gers taking a 2-1 lead to Switzerland to face Servette.
He continued: "It's a dangerous game with a dangerous opponent. We know that and we will have to be at our best - we need to be defensively as strong as we were today, and we need to be decisive in the final third.
"Scoring four goals today will certainly help us but we have to go there with the right mentality out of possession first, be strong, hard to play against and show our quality.
"It is a hugely important night for everybody and safe trip to all the fans that are going across to Geneva this week."