Trailing 2-1 from the first leg, Ajax stunned the holders by winning 41 at the Bernabeu to win 5-3 on aggregate.
“I didn’t come to the club at such a difficult moment to give up,” Solari said.
“What we must do is remain as calm as you can at such a difficult moment and also take it around with the best character.
“Madrid is bigger than any people – it always returns – and returns even stronger.”
Former Real midfielder Solari replaced Julen Lopetegui as boss in November, signing a contract before 2021.
The last-16 leave marks the first time the 13-time winners have failed to reach the quarter finals since 2010, also defender Dani Carvajal worries the”season has ended” for a golf club who have won the past three Champions League finals.
“I’ve never felt as fortunate as this, I don’t know how to explain it,” said Carvajal. “In one week everything moved , and all of it afterwards games in your home.
“It’s clear the growing season has ended but we will keep on working in the league because that’s what we have to do and we all have to become professional.”