The Magpies reached the quarter-finals of the Europa League in 2012-13 but finished the season in 16th place in the Premier League table.
Everton are currently 14th in the table ahead of Sunday's Premier League clash against Newcastle.
But in another interview he says he is desperate to see Newcastle United back in Europe – despite the pitfalls.
Asked if he wanted to qualify for Europe, Carver said: “Cast your mind back to playing against Benfica at their stadium.
“I’ve got photos on my phone because it was a great occasion.
“We went there trying to win it. Can you imagine if we had won it?
“People are critical of us not trying to win cups. With me, you couldn’t be any further from the truth.
“I’ve been in the Champions League situations, and Marseille in the semi-final of the UEFA Cup.”