Ritchie scored his first goal for the club in Wednesday night’s 4-1 win over Reading at St James’s Park.
The winger, signed from Bournemouth this summer for £10million, netted from the spot to put Newcastle 2-1 ahead early in the second half.
And Dwight Gayle made certain of all three points with two more goals.
United, beaten in their first two Championship fixtures, take on Bristol City at Ashton Gate tomorrow looking to build on the victory.
Ritchie says playing at St James’s Park – there was a crowd of 48,209 there for the Reading game – is everything he hoped it would be when he signed for the club.
“It’s fantastic support, and we need them because it’s a joy to play in front of the fans,” said the 26-year-old.
“They’re passionate and we want to be passionate on the pitch as well. Hopefully, this win was an inkling of that.”
The victory eased the nerves on Tyneside after defeats to Huddersfield Town and Fulham.
“I think we owed it to the fans to get a win,” said Ritchie. “There was obviously a lot of expectation from day one, but that’s three points on the board now and lots of hard work still to do.
“We need to make sure that we keep working as we have done this week, with the same mentality, and make sure that we build on this.”
Gayle had a penalty saved against Huddersfield – he netted from the rebound – and Ritchie took the ball after Chris Hunter hauled down Yoan Gouffran in the box.
And Ritchie has suggested that there is not a designated penalty-taker this season, as several players are prepared to take spot kicks.
“Dwighty took the one at the weekend and missed it, but I mean it’s only one,” said Ritchie.
“We’ve practised them in training, and there’s a few of us that fancied taking them. I fancied this one, and luckily I tucked it away there.
“Obviously, I’ve been looking forward to scoring goals here from the minute I heard of the interest, so that was a pleasing moment as you’ll have seen with my celebration.”
Ritchie had started the Huddersfield game from the bench, having been unable to train last week because of a tight hamstring.
But Benitez reluctantly “risked” him in the second half.
“I felt my hamstring a little bit against Fulham and didn’t train last week, so hopefully that’s behind me now,” he said.
“Hopefully, I’ll stay in the team and continue to make an impact.”
Ritchie – who has experience of the Championship from his time at Bournemouth – says he and his team-mates won’t be getting carried away after one win.
“You know what football’s like – one minute we’re written off, then we win one game and I expect the odds will probably get slashed again,” he said.
“We won’t be taking too much notice of that. We’ll be keeping our feet firmly on the ground, working hard with a good mentality.
“In this dressing room we have top players, a very good squad, but the key is mentality.
“If our mentality is right, and we work harder than the other teams, there’s no reason why we shouldn’t win most games.
“But it’s not going to be easy.”