The Magpies, who had gone eight league games without a win since the start of the campaign, finally closed out a roller-coaster of a game at St James' Park as £14.5million summer signing Georginio Wijnaldum plundered four goals.
McClaren said: "It's Newcastle, is it possible to make any sense? That's what we are fast discovering. But I think that was just reward. I'm so pleased for the players, so pleased for the fans.
"Like we have said all along not to get too down and after tonight, we are not going to get high. There's a lot of work to do, but it shows today when it comes together what we are capable of doing."
A victory which lifted Newcastle to the relatively heady heights of 18th place in the table, came as a huge relief to McClaren and his players seven days before their derby trip to fellow strugglers Sunderland, and provided the club's famous 88-year-old tea lady, Kath Cassidy, with the perfect send-off after 52 years' service.
But it came in nerve shredding fashion as Wijnaldum struck twice and Ayoze Perez once before the break only to see Dieumerci Mbokani and then Nathan Redmond keep the Canaries within touching distance.
However, with the visitors pushing for an equaliser, the home side prospered on the break with Aleksandar Mitrovic extending their lead before Wijnaldum helped himself to two more.
Asked about his emotions, McClaren said: "It's relief, and then thinking we have got to prepare and we have got to do it again next week.
"It's very short, the feeling is very short. Football is all about momentum and you can have momentum going the other way - which we have had. We want this one to go forward.
"There's a long way to go, a lot of work to do, but today showed the potential and showed the supporters at home that this is what we are capable doing."
Wijnaldum because the first Magpies to score four goals for the club since Alan Shearer put five past Sheffield Wednesday in an 8-0 demolition job in September 1999.
McClaren said: "You saw today what he is capable of doing, which is why we brought him here. He can be and will be and showed today that he's a Premier League player."
For Norwich boss Alex Neil, it proved a frustrating trip to the north-east.
He said: "Offensively, we looked dangerous, scored two really good goals, hit the post twice, had other good opportunities to score; but defensively as a team...
"To be honest, I thought the game was wide-open - it was a bit like a basketball match. I thought both teams were wide-open.
"It could have ended pretty much 8-8, but the opportunities we had, unfortunately we didn't score, we hit the post or whatever, and pretty much most of the opportunities Newcastle had ended up in the back of the net.
"I thought both teams were really, really open and we could have score four, five or six ourselves.
"For them to score six based on the game itself, you could argue it was harsh, but we have got to defend better."