Everton fans gave their side a warm welcome before kick-offIs Everton's unbroken Premier League stay about to end this season?
But despite a demoralising second-half collapse against the Magpies to extend their run to one win in the last 10 games, Dyche is confident his side can avoid relegation.
After replacing the sacked Frank Lampard in January, the ex-Burnley manager's reign started in perfect fashion with a 1-0 win against table-toppers Arsenal.
But there has been little to celebrate since.
"I think we can do it," replied Dyche when asked if they can stay up. "It is a similar side to when we beat Arsenal, so there's evidence it can be done.
"We need to bring the edge of that performance. We had that in the first half and it was a really good performance. Goals change games, not just the scoreline but the feel of the performance.
"You are still in it at home but you cannot let it change the whole performance."
Everton have to correct mistakes 'quickly'
Everton supporters did their best to get behind the team before kick-off, welcoming the team coach into the stadium by lining the street outside and chanting and lighting blue flares.
The backing continued in the first half when the side were on top, but their optimism was sapped once Callum Wilson scored the opening goal.
The Toffees have scored multiple goals in just one of their 17 home games this season so a comeback looked highly unlikely, with further goals from Wilson - a magnificent second - Joelinton and Jacob Murphy.
Dyche added: "Very disappointed in the end. The first half we did everything I thought what was right against a good Newcastle side. It was all there other than the goal.
"We nearly scored a goal just before half-time and the second half we start brightly but, as soon as the second goes in, the game goes away very quickly.
"It happened against Fulham and we have to correct that quickly.
"It is about us, we have to correct the mistakes we have made in the last few weeks. We can all talk the talk but it is about walking the walk."
Everton face a massive game next against fellow strugglers Leicester on Monday, with the Foxes a point and place above them in the drop zone.
Asked if the manner of the defeat meant his side have lost the fans, with many leaving well before the end of the match, Dyche said: "I don't think so. The fans have been terrific, they are amazing here. They will be backing the club until the end.
"I can't decide for 40,000 people, but they will support the club until the end of the season."
