The forward, who joined City from Bournemouth for $A130 million last week, struck the opening goal in the semi-final first leg at St James' Park on Tuesday (Wednesday AEDT), with substitute Rayan Cherki scoring the second in extra time.
Semenyo also scored on debut in the 10-1 rout of Exeter in the FA Cup at the weekend.
"The whole environment here is perfect," Semenyo said.
"Everyone is confident and wanting to achieve the best.
"I've just come into that and they've helped me with my confidence and they've made me feel welcome."
It could have been even better against Newcastle for the Ghana international, who saw a brilliantly taken back-heeled goal ruled out for a marginal offside.
The 26-year-old Semenyo is already looking like a shrewd buy for City after establishing himself as one of the Premier League's top talents for Bournemouth. He scored 10 goals for the Cherries this season.
"He's not just a very good player, but a very good guy, which helps, which fits into the team," City captain Bernardo Silva told ITV Sport.
"He's a fantastic guy who wants to play collectively, wants to help, wants to have fun, and we are delighted with the way he's started."
Semenyo has added another dimension to City's attack as Guardiola targets four trophies this term.
The League Cup could be the first of those, with City holding a two-goal advantage against holders Newcastle heading into next month's second leg at their Etihad Stadium.
Semenyo converted from close range with a simple finish in the 53rd minute to put City ahead. He looked like he'd scored a far more spectacular second with a back-heel volley - but after a lengthy VAR check, it was ruled out because Erling Haaland was in an offside position.
City had to wait until the eighth minute of added time to double the lead, with Cherki slipping a shot past Newcastle goalkeeper Nick Pope from inside the box.
That goal has left Newcastle with a mountain to climb if they are to keep the trophy they won last year to end a 70-year wait for major domestic silverware.
Eddie Howe's team had its chances, with Yoane Wissa and Bruno Guimaraes both hitting the frame of the goal within seconds of each other in the second half.
City are eight-time winners of the League Cup, with Guardiola lifting it on four occasions. City last won it in 2021.
City's four-pronged trophy hunt this term follows last season when they finished empty-handed for the first time in eight years.
Trailing Premier League leaders Arsenal by six points, second-placed City are also well-positioned in the Champions League, and are into the fourth round of the FA Cup.
In the first leg of the other League Cup semi-final, Chelsea host Arsenal on Wednesday (local time).
