Costa helped to fire Atletico to a stunning La Liga title win in 2013-14, scoring 36 goals in all competitions.
However, a thigh injury dogged him during the final weeks of the campaign and he lasted only nine minutes against rivals Real Madrid in Lisbon.
It would prove to be Costa's final appearance for Atleti before moving to Chelsea, and his team-mates went down to a 4-1 extra-time defeat after Sergio Ramos equalised for Madrid deep into stoppage time.
"If I had it all over again, he'd play the final from the start again. How could our best player not play?" Simeone told AS of the player he looked to bring back to the Vicente Calderon last year.
"He wasn't injured! Did you see the 100m sprints he was doing out on the pitch?
"I said: 'If this lad can give me 45 minutes in the Champions League final...' It's Diego Costa!
"It's like Messi being at 50 per cent and not playing for Barca in the Champions League final. For us, Diego Costa was our Messi."
Simeone said losing to Madrid in Europe's showpiece final in both 2014 and 2016 affected him "deeply" and feels his players' feat in recovering impressively from such setbacks will be remembered fondly for years to come.
"Any other team that lost two finals in that way - other than Real Madrid, Barcelona or Bayern Munich, clubs that are so used to playing finals - would have gone into decline," he said.
"Time will bear out the importance of what we achieved. It'll be historic, legendary."
Atletico knocked out Barcelona and Bayern on an incredible run to last season's final against Madrid but Simeone believes those heavyweights retain in-built advantages over the rest of Europe's top-tier sides.
Zinedine Zidane's defending champions must get past Bayern in this season's quarter-finals, while Barcelona face Juventus.
On paper, Atletico have a more favourable draw against Leicester City - not that it has persuaded Simeone there is any greater chance of besting the trio.
"To be honest, I don't think it's possible," he said. "You've named three clubs that are different to the rest, particularly because of the footballers they have.
"Don't ask me exactly how, but their history sets them apart as more powerful in every area.
"To contemplate getting to that level, we'd need years more of what's happening to us now.
"Atletico have the 15th highest budget in Europe but compete in footballing terms. And it hasn't been enough to win the Champions League."