Howe's side slumped to 12th in the Premier League following the dramatic 2-1 loss at St James' Park in their last game before the international break, as promoted Sunderland achieved a league double over their neighbours.
The defeat came days after Newcastle capitulated in spectacular fashion at Barcelona in the Champions League, suffering a humiliating 7-2 thrashing after playing out a 1-1 draw in the first leg against the Spanish side.
"I don't have a stance on his future. What I can tell you is that the derby loss hurt," Hopkinson told reporters.
"We take it seriously. There's nothing within us that thinks, 'Well, it's just three points and on we go'. It has resonated.
"I spent a couple of hours in a one-on-one lunch recently with Eddie and we talked through a multitude of things, including that."
Howe, who signed a long-term contract in 2022, has seven games to improve Newcastle's position in the Premier League standings if they are to play in Europe next season. They sit six points behind sixth-placed Chelsea.
Hired in 2021, Howe has led Newcastle to Champions League qualification twice and ended the club's 70-year trophy drought when they won the League Cup last season.
"Eddie is our manager. I expect to have a great run to the end of the season here and we will talk about the future when it's time," Hopkinson added.
"Right now, we're focused on this season's competition."
Newcastle announced record revenues of 335.3 million pounds for the year ending June 2025.
The club said commercial income rose 44% despite not playing European competition during the accounting period and they posted a profit after tax of 34.7 million pounds.