The Gunners arrived in the north-east knowing anything less than a win would leave them open to being overtaken by great rivals Tottenham in the race for fourth place, but Laurent Koscielny's goal in the first half saw Arsenal over the line.
Arsenal can now look forward to a 16th successive season playing among Europe's elite - providing they come through a qualifying match - and Wenger was fulsome in his praise after seeing his players end the season in searing form.
A 2-1 loss to Spurs left Arsenal seven points adrift of their north London foes in early March, since when they have taken 26 points from a possible 30 to end the campaign a point clear of Andre Villas-Boas' troops.
"They are special. I've told them many times but they've shown it in the last two months they've been absolutely exceptional," Wenger said of his players on Sky Sports 1.
"We have shown character and attitude.
"We make 73 points, that's three points better than last season.
"I've had many groups in my life and the focus, the desire to do well, was exceptional. It's one of the best groups I've had in my life on that front."
He said: "Since February 1, we have taken more points than everybody else in the league, and I don't believe that's just down to coincidence, but just to the fact that the group has grown, this team has grown through the season.
"We lacked belief for long periods because we couldn't win a big game, but the Bayern [Munich] game changed our season away from home.
"In the last three months, I believe we have been remarkably consistent. We have won every away game, so it is a good springboard for next season, to transfer that belief into the start of next season.
"That means we need to have stability and strengthen our group if possible because there are many clubs out there with a lot of money, so the competition is very hard and there is not as much talent as money today in football."
Asked if silverware now needs to be the next aim after another barren campaign in that area, Wenger added: "We want of course to do that next season, but let's not forget the consistency we have shown over the years to get into the Champions League."
He said: "It means to us to be able to play with the top teams in Europe - that's what you want.
"It means as well that it's easier to bring in players when you have a chance to be in the Champions League - let's not forget, we are not in yet, we have to qualify and that is always a very tricky round for us.
"But at least we have a chance."
Discussing his plans for squad rebuilding in the summer - when a sizeable budget is expected to be at the Frenchman's disposal, he added: "We want to have additions to the squad but keep the structure, spirit and quality of the squad we have now.
"We will be out there in a very pro-active way."
Newcastle had perhaps shaded the first half without testing keeper Wojciech Szczesny unduly, but the Gunners gradually wore them down and might have cemented victory at the death when Walcott out-stripped a leggy defence and stabbed the ball past 38-year-old keeper Steve Harper, making his final appearance for the Magpies after 20 years on the books, only to see his effort come back off the post.
Manager Alan Pardew was at least able to comfort himself with a much-improved display after thumping home defeats by Sunderland and Liverpool in their last two games.
But ultimately a 16th-placed finish with 41 points - 24 fewer than his side managed last year when they ended the campaign in fifth - was a major disappointment, with the demands of a Europa League campaign taking their toll.
Pardew said: "It was the depth, really, and quality we need to improve on. But next year, we haven't got that pressure and we can go week to week in this Premier League.
"But we are not going to be foolish enough to think that we don't have a couple of issues to sort out in the team - not major issues, but certainly one or two players to add to offer us a different look."
Asked about his own future after weeks of speculation by disgruntled fans, Pardew said: "I'm pretty confident I'll be the manager here.
"I love being the manager and I will be speaking to [owner] Mike [Ashley] and [managing director] Derek [Llambias] this week to make sure we get a response and the right reaction."