The Spaniards went behind due to an own goal in the 18th minute but never lost their composure, cantering into the quarter-finals thanks to goals from Rodri, Fabian Ruiz, Nico Williams and Dani Olmo.
"I think Spain are the favourites for this tournament and they will become champions. It's a pity that we met this team, but it's okay, it's not the end. We will come back stronger," Mamardashvili told reporters.
"Of course, it's sad that we lost in the round of 16, but we should also be happy about it, because not long ago we couldn't have imagined that we would reach this far," he added.
The Georgians became one of the feelgood stories of the tournament by beating Portugal 2-0 in their final Group F game to make it to the knockout stages, all while trying to play expansive football against more illustrious opponents.
Captain Guram Kashia said his side were disappointed to be heading home, and that the loss of leading striker Otar Kiteishvili to injury proved a big blow.
"We played well in the first half (against Spain), in the second, after we lost Kiteishvili, the game changed. In the end, we conceded goals and said goodbye to the championship, but we are happy that we represented our country with dignity," Kashia said.
"We are proud of how we represented our country at such a high-level tournament. We got to the European Championship for the first time, and it was an amazing adventure. I am once again proud of our game," he added.