It's about what you would expect. The North Vietnamese government used the incident as propaganda, especially abroad, in their effort to delegitimize the American role in the war and the South Vietnamese government. It was used domestically as well, and still is to this day. The other communist states did likewise. You may recall that back during the Korean War, the PRC and North Korea fabricated charges that the US military was using chemical weapons (they accomplished this by torturing US pilots and having them give 'confessions'). So this was a case where there was a real war crime, and it was exploited against Washington.

Now, if you are asking if North Vietnam was surprised or morally taken aback? No. The war had been going on since 1945, and the Viet Minh and later North Vietnam had assassinated tens of thousands of their opponents and been guilty of civilian atrocities as well. Most famously, during the 1968 Tet Offensive the Viet Cong and North Vietnamese troops executed several thousand Vietnamese residents of Hue, most of whom were connected to the South Vietnamese government. This was a systematic, planned event (unlike My Lai). The incident is highly censored in Vietnam to this day -- most people in Vietnam do not even know about it. The memorial and graveyard for the victims was destroyed after 1975.

The My Lai massacre continued to play a powerful role in the government's propaganda after 1975. Hard-line communists or pro-China elements of the Vietnamese Communist Party would point to My Lai as a warning that Vietnam should avoid too much liberalization and not align with the United States. Instead, they argue, Hanoi should stay close to Beijing. When the book Kill Anything That Moves by Nick Turse -- which is a poor history with significant problems, I should note -- came out recently, Vietnamese Communist Party hardliners specifically touted that book as proof that Americans were not trustworthy, and that they should avoid a closer US-Vietnam alliance.