Albion's battling win over Portsmouth, courtesy of goals from Geoff Horsfield and Kieran Richardson, sparked unprecedented scenes of jubilation to the blaring backdrop of 'The Great Escape'.
The win was enough to extend their top-flight status as the three results elsewhere went their way. And Robson praised his players for becoming the first team in history to survive after being bottom on Christmas Day.
Robson said: "This is the best and the reason I say that is when you are at Man United you are expected to win trophies because you are playing with great players. There is no expectation whatsoever here apart from expecting us to go down so that made it very difficult for us.
"But the players have responded and kept battling no matter what the circumstances so that is great credit to all the players."
Robson appeared to have taken on mission impossible when he took charge of the rock-bottom Baggies in November and failed initially to win over the home fans.
But his acquisitions of the likes of Kevin Campbell and Kieran Richardson proved vital in fashioning the unlikeliest of escapes.
"We have had to cope with all this stuff about you can't survive if you are bottom at Christmas, and a lot of weaker characters could easily have given that as an excuse.
"But they haven't done that. They have really fought hard for each other and the whole club have got behind the players and really believed."
Robson said he had some success in avoiding news from elsewhere as The Hawthorns see-sawed between jubilation and spells of eerie silence.
But he admitted inquisitiveness finally got the better of him in the final 10 minutes, where the Baggies' lead looked set to count for nothing because of events at The Valley.
"The only time it affected me was with 10 minutes to go and people started saying Palace were winning.
"You start thinking is not going to be. But I always said we had to concentrate on our own performance and make sure we get the three points. We did that and we did it really well."
Jubilant midfielder Jonathan Greening singled out captain Campbell for special praise.
Greening said: "The team spirit over the last three or four games has been amazing and you could see out there how much it meant to us. We have been a really tight squad for a lot of months now and Kevin has been a great captain and held us all together."
Pompey almost grabbed the lead in the 49th minute when O'Neil's corner was flicked across the face of goal by Kamara and out for a goal-kick.
Ten minutes later Albion suddenly moved into pole position in the yo-yo race to stay up when Horsfield drove Gera's cross under Pompey keeper Jamie Ashdown to put them ahead - shortly after he replaced Greening.
The strike caused a huge wave of relief at The Hawthorns but contrasting news of events elsewhere silenced the home supporters quickly.
With Albion starting to confidently hold their own, more and more minds switched elsewhere and Richardson's 75th minute second for Albion almost proved a distraction.
The remaining 10 minutes were played out in some of the most bizarre circumstances imaginable with rumours and counter-rumours sparking short phases of celebration and despair.
Then after one minute of agony as The Hawthorns waited to hear its Premiership fate, a final whistle in south-east London sparked extraordinary scenes of celebration.
Norwich, Southampton and Crystal Palace were bidding farewell to the Premiership - but the Baggies lived to fight for another season at least.
: Kuszczak, Albrechtsen, Gaardsoe, Robinson, Clement, Gera, Wallwork, Richardson, Greening (Horsfield 58), Earnshaw (Kanu 84), Campbell.
: Ashdown, Primus, De Zeeuw, Stefanovic, Taylor, Keene (Mezague 81), Cisse, Hughes (Skopelitis 50), O'Neil, Fuller, Kamara (Rodic 65).
: M Riley (W Yorkshire).