The Scottish champions were humiliated 6-0 by Atletico Madrid at the Wanda Metropolitano on Tuesday night.
They are now sitting at the bottom of their Champions League group and need to win their last two games to stay in Europe beyond Christmas.
However, Grant stressed that he wants Celtic in the Champions League again next season as he feels there is nothing embarrassing about crashing out of the competition early.
He insisted that he wants the Bhoys to win the league again and be in Europe’s elite competition again next year.
The Celtic legend is not keen to see his former team ply their trade in Europe’s second or third-tier competitions.
Grant said on the Go Radio Football Show: “You never get embarrassed if you go out of the Champions League.
“Win the league here, it’s the most important thing here to get into that Champions League.
“I don’t care if they lost every game in it. I’d rather be in the Champions League than the [Europa] Conference League that everyone keeps going on about.
“The Champions League is for the champions and that’s where you want to be, playing against the best.
“That’s the only way to learn.”
Celtic are sitting at the top of the Scottish Premiership standings and will again be in the Champions League if they retain their title this season.