The 22-year-old Frenchman completed his £13million switch from Marseille on Wednesday evening to become the Magpies' fourth major acquisition of the transfer window, a combined total spend in excess of £50million.
However, while the club continues to be linked with QPR striker Charlie Austin and a series of central defenders - Monaco's Aymen Abdennour is the latest name to be churned out by the rumour mill - McClaren is not expecting further additions.
He said: "I'm very pleased with what we have got, very pleased. I think that's it for now - but how many times have you heard, 'That's it for now' with 10 days to go of the window?
"We are not expecting, we are not chasing anything. We are not trying to make things happen. Usually with 10 days to go, things might happen.
"But at the moment, we are delighted with what we have got and let's get to work with them. That's the key thing now: they're in, let's get them working and let's get them playing.
"I don't think any manager is ever entirely happy, but I'm happy with what we've got to work with. There comes a point where we just have to sit down and stop and say, 'You know what, this is what we have, and now we have to work and develop them, and try to make them into a team that is hard to beat and no one wants to play against'."
Georginio Wijnaldum, Aleksandar Mitrovic, Chancel Mbemba and Ivan Toney have also been drafted in during a busy summer with Remy Cabella heading for Marseille on an initial loan deal as part of the Thauvin transfer.
McClaren is confident that represents a genuine statement of intent by controversial owner Mike Ashley, who publicly promised significant investment at the end of last season.
McClaren said: "Absolutely, without a shadow of doubt. After Mike Ashley's words, I think people were doubting, and those doubts were still there at the beginning of pre-season, especially when I first came in.
"There were a lot of doubts and comments that it was all talk, but I think the club have delivered. They've absolutely delivered 100 per cent with the quality that we've got."