The Magpies finally secured their first league win at the ninth attempt as they thrashed Norwich 6-2 on Sunday.
And McClaren is understood to have the full support of owner Mike Ashley.
McClaren said: "You are going to get protests and people not happy when you change the coaches. There is so much potential, but still a long way to go."
The former England manager's only win before the game was in the League Cup against Northampton.
Both club and coach had been on a horrendous run of results before beating the Canaries.
Newcastle were on their longest winless start to a season since 1898 and had won just once in their previous 19 league games.
McClaren had won just twice in his past 21 games as boss of the Magpies and Championship side Derby County, but his job would not have been under threat even if they had lost against Norwich.
"It's Newcastle, is it possible to make any sense? That's what we are fast discovering," said McClaren after the victory.
"We knew a win was around the corner, but we didn't know when it would come.
"We played some really good football. We kept the faith with the players - everyone around us is saying what they've been saying, but we've got to keep tight.
"Against Chelsea and Man City we looked like scoring. Today it was the same but we were clinical in our finishing."
A frantic first half saw five goals scored in the space of 20 minutes, as both sides' defences struggled.
Netherlands international Georginio Wijnaldum became only the second Newcastle player - after Alan Shearer - to score four goals in a Premier League game for the club.
"What a game in the first half. I didn't know what was happening," McClaren added. "We looked like scoring and conceding. We then settled down and produced some quality.
"The front four were excellent, especially Gini Wijnaldum. Moussa Sissoko showed strength and power and he showed why he is coveted by the top four.
"I thought the score could have been anything. We rode our luck and defended quite well. On the break we were terrific."
Newcastle head coach Steve McClaren said he has had "enormous support from within the club" despite his side's difficult start to the season.