Jurgen Klopp's side took the lead at St James' Park through a stunning goal from Philippe Coutinho, only to concede a soft equaliser to Newcastle striker Joselu seven minutes later.
The game summarised Liverpool's season to date; they squandered a number of opportunities in the first half, were too easily opened up by their opponents and then struggled to find any attacking fluency after the interval.
They have now won just once in their last seven outings in all competitions, a disappointing run of form prior to a home fixture with arch-rivals Manchester United straight after the international break.
"If you come away with a 1-1 result, that's obviously a disappointing feeling. You start to look at what you could have done better," Mignolet told the club's official website.
"I think we played well, we deserved to get the victory; we created chances. But it is how it is at this moment in time, we have to take it.
"It's disappointing and frustrating but we have to keep looking forward, keep our heads up and make sure when we come back after the international break we go again against Manchester United, which is a big game and something to turn things right for us."
However, the 29-year-old is already looking forward to a mouth-watering match on his return to club duty, as he hopes to put an end to Manchester United's unbeaten start to the Premier League campaign.
“Everybody will be away in another environment and when they come back we’ve got that one to look forward to," Mignolet added.
“I’m sure everybody will be focused on their international duties now but when they are back they have a big game to look forward to. We will be ready for it.”