The CONCACAF Champions League winners face the Club World Cup surprise package for third place in Marrakech this weekend, and will be heavy favourites to claim victory.
Cruz Azul suffered a 4-0 defeat to Real in the semi-finals, but Tena believes there were plenty of positives to take from the encounter, which he hopes will serve his players well against Auckland.
"Although we've simply got to acknowledge that Madrid were by far the better team, it was a great experience to play against such a strong side, and we can learn plenty from it," he said.
"Now our full attention will be on the match for third place, a game we want to win no matter what."
Auckland have enjoyed a remarkable run at the event in Morocco, and only narrowly missed out on a place in a final.
The prospect of going up against Real for the trophy will have seemed unlikely for Auckland when they entered this competition at the earliest possible stage - requiring penalties to see off Moghreb Tetouan.
An unexpected 1-0 victory over ES Setif followed to inspire hope that Auckland could achieve the unthinkable, but the New Zealanders' challenge came to an end on Wednesday when they were beaten 2-1 by San Lorenzo after extra time.
Nevertheless, coach Ramon Tribulietx has hailed his players' efforts during the tournament, and is determined to enjoy every last minute.
"We were brave, had a lot of possession against the South American champions, and showed that we can compete at this high level and play good football," he said. "I’m very proud of my players - they'd have deserved to win.
"It's fantastic to be at this tournament and show the world what we're capable of."
Chairman Ivan Vuksich told stuff.co.nz: "I'm disappointed, but at the same time I'm really, really proud of what they've achieved.
"It's beyond my wildest dreams, I'm sure it's beyond the wildest dreams of a lot of people at the club."
Gerardo Torrado, who saw a penalty saved in Cruz Azul's semi-final, is the only man to have scored more than one goal at the tournament having converted two other spot-kicks, and will be looking to cement his status as top scorer.
