The Tyneside club had to beat the Toffees and hope that either Tottenham or Arsenal slipped up to snatch a place in the top four, but in the end both north London sides won their fixtures.
Goals from Steven Pienaar, Nikica Jelavic and Johnny Heitinga gave the Merseysiders a comfortable advantage before Tony Hibbert put through his own goal to give the visitors a consolation.
Despite not breaking into the top four, Alan Pardew spoke of his pride at his side’s achievements this term.
“It has been a tremendous season. We have played every game to try and win,” he revealed to Sky Sports.
“Even here, at 2-0 down, we were pushing the game. We are very proud of what we have achieved.
“But it is something to build on. We have got to improve in certain areas. But we have made great inroads to the bigger clubs. That is credit to the players.
“We have got a European campaign on top, so it won’t be easy. But it has been a magnificent effort.
“To finish above the likes of Everton, Liverpool and Chelsea, it is a fantastic achievement,” he concluded.
By Gareth McKnight