Croatia's previous heaviest loss was a 6-0 defeat by Spain in 2018. Modric, the country's most-capped player, said the manner of the defeat by England was unacceptable.
"It is difficult to find an explanation for such a performance without duels, fouls, aggressiveness, togetherness... I've been here for 20 years, but for the first time I feel ashamed after a game," he told Jutarnji.
"You can lose, or play against an opponent who is better - and they are right now. But in any case, losing like this and squandering the reputation we've built over the years is unacceptable.
"You can't play football like that. You can't play with two players less, you can't play like this, and we looked like we had 4-5 players less. A catastrophic night," the 41-year-old added.
Croatia next host Spain in Split on Tuesday. The world champions have a 100% record so far in the Nations League and won their first meeting 4-1 on Tuesday.
"We need to pull ourselves together, stay together because a new difficult game awaits us," said Modric. "And we have to show our true colours, that there is defiance and pride in us, desire, willingness, togetherness, these things cannot be lost overnight."
Croatia are third in Nations League A, Group Three.