The Seagulls needed to win at Aston Villa or better Newcastle's result but Jack Grealish's late equaliser earned Villa a 1-1 draw, while Newcastle beat Barnsley 3-0 to be crowned champions by a point.
Murray, who netted his 23rd goal of the season at Aston Villa, said: “It is a disappointed dressing room, but give it 24 to 48 hours and we’ll reflect on what we actually have achieved this year, even though right now the feeling is disappointment.
“Obviously the group that were here last year was disappointed, and ultimately getting into the Premier League was our main aim and we’ve done that.
“Looking at the last three games we had a chance to win it and unfortunately that wasn’t to be, but we need to congratulate Newcastle because they’ve stuck at it and we’ve got to be humble in defeat.”
Grealish's 89th-minute leveller went through a crowded penalty area and then the legs of Albion keeper David Stockdale but Murray said: “I don’t think anyone is looking at David for making a mistake; he’s rescued us time and time again this season and been absolutely magnificent.
“People may look at it and say it’s David’s mistake, but then we look at it and say maybe not. Maybe three moves beforehand we should’ve stepped up and pressed harder, popped out of position and stopped the shot, but it was just one of those afternoons and it wasn’t meant to be.
“It went in in the 89th minute and left us with a mountain to climb, so it just wasn’t meant to be.
“We had one or two chances ourselves, but as I said that’s football and Aston Villa are a very good side. I think they’ve underachieved this year and we’ve struggled against them drawing 1-1 twice. They showed what a good side they are.”
Finally, reflecting on reaching the Premier League, Murray said: "It's what the club's wanted for a long time and in 48 hours, when the disappointment of this wears off a little bit, we will be a proud bunch of guys."
Don't miss out on all the latest breaking news where you live.
Here are four ways you can be sure you'll be amongst the first to know what's going on.
1 Make this website your homepage
2 Like our Facebook page at facebook.com/pages/Sport-Sussex3 Follow us on Twitter @SportSussex
4 Register with us by clicking on 'sign in' (top right corner). You can then receive our daily newsletter AND add your point of view to stories that you read here.
And do share with your family and friends - so they don't miss out!