Scholes had put United into the lead before Giggs proved to be a last-gasp hero by converting Ashley Young's cross deep into stoppage time.
Scholes, 37, came out of retirement last month and has seamlessly slotted back into the Premier League, while Giggs, 38, scored the winner on his 900th appearance for United. The former Wales international has already signed a new one-year contract for next season and it appears likely Scholes will do so too.
Sir Alex said: "Scholes and Giggs are the best players this club has ever had. Given the career Ryan has had, to score the winning goal with the last kick of the game ... I think he deserved that.
"We could have played him against Ajax on Thursday but this game was more important and I knew we would need all our experienced players and Ryan and Scholesy in particular. That experience is really going to help us in the next couple of months.
"We won't get nervous, that's for sure. We're used to being in this situation. You saw that when we conceded an equaliser. How did we react? We started playing again and got the winner.
"Everyone knows we never give in. No matter who plays us, they know they will have to battle right to the death. But we were lucky because Norwich were the better team. They had a lot of thrust about them, they were determined and kept crossing the ball into our box."
Giggs added: "It's a great day for me personally - 900 games for United is a real honour and to score the winner as well, it doesn't get any better than that. I first scored at Norwich in the first season of the Premier League but this one feels even better.
"It's always great to score the winning goal and I have to make sure I savour days like this."
Scholes, meanwhile, admits Manchester United may have to win all of their remaining 12 Premier League games as they aim to hunt down rivals Manchester City in the race for the title.
"There is no point drawing games so we were throwing everyone forward going for that goal, and I am sure we will do the same thing again,'' Scholes told MUTV.
"Of course, three points instead of one is a big difference. That is what we are here to do. We realise we may have to win every game to win the league, but we are ready and prepared to do that. Hopefully, we can do it.''