The Argentinian took over from Gregorio Manzano in December 2011 and has enjoyed an inspirational trophy-laden spell, with last season's title triumph the pinnacle.
Atletico were finally presented with the trophy before Saturday's game at Vicente Calderon but, having drawn their opening game at Rayo Vallecano, they again struggled to produce much of an improvement as the banned Simeone watched from the stands.
German Burgos deputised on the touchline once again and it did not take long for Atletico to race into the lead, with headed goals from Miranda and Mario Mandzukic making it 2-0 in 25 minutes.
Abraham brought Eibar back within touching distance after capping off a fine move with a delightful finish and the visitors continued to improve after the break.
Atletico escaped late on as Eneko Boveda headed just wide of the target and the nervous hosts held on to a slender win in unconvincing fashion.
Without Simeone patrolling his technical area, proceedings were a little tepid early on, however the score was only level briefly.
Koke, one of the stars of Atletico's title-winning campaign, fired a dangerous corner delivery in towards the near post and Miranda steered home with a glancing header after 11 minutes.
The hosts were seemingly disappearing from sight as Mandzukic nodded in Gabi's free-kick to open up a two-goal lead in the 25th minute, but Eibar soon brought themselves back into the contest in stylish fashion.
After cutting in from the flank, left-back Abraham played a give-and-go with Angel, before also linking up with Mikel Arruabarrena on the edge of the area and caressing an exquisite first-time right-foot finish into Miguel Angel Moya's top-right corner.
Atletico nearly re-opened their two-goal advantage eight minutes before the break, but Xabi Irureta tipped Raul Garcia's deflected 20-yard effort on to the crossbar.
The hosts appeared to struggle with Eibar's forceful pressing early in the second half, with the Basque side also enjoying much more of the ball than they did before the break.
But neither team looked particularly convincing going forward, with chances becoming increasingly infrequent.
Eibar eventually forced Moya into action with 24 minutes to go and the former Getafe man stuck a foot out to stop Angel's effort squeezing inside the post.
The visitors saw further chances go begging in the 75th minute as Boveda headed agonisingly wide from six yards and Angel prodded wide when one-on-one to ensure Atletico ultimately clung on to a far-from convincing win.
