Albion led 2-0 at half-time through Murray’s double but Fulham came out strongly in the second half and goals from Calum Chambers, Aleksandar Mitrovic (two) and Luciano Vietto took the Cottagers to a 4-2 Premier League victory.
The Seagulls have won just one of their past nine top-flight games but are still seven points clear of the relegation zone and host Watford at the Amex on Saturday.
Murray felt there were positives to take from the Fulham defeat but is already looking ahead to the clash with Watford.
He said: “As well as the negatives, there’s definitely positives to take. It was probably one of our best first halves of the season, so it’s not that we’re not playing well.
“We’ve had a difficult run of fixtures recently and we take that into consideration. We’re not getting down over tonight. We’re disappointed 100 per cent but come tomorrow it’s about putting it to bed and working towards Saturday.
“There’s no time to dwell in the Premier League. If you start dwelling on bad results and feeling sorry for yourself, then it’s not a good thing.
“It’s about putting it to bed as soon as possible and we’ve got another opportunity on Saturday to get three points and that’s what we’ll be trying to do.
“We’ll do our homework, we’ll anyalyse it and we’ll try for it not to happen again.
“By Thursday morning, come training again, we’ll be looking towards Watford and try to get three points.”
Albion lost a two-goal lead on the road for the second time this year, after drawing 2-2 away to West Ham at the beginning of January, and Murray said: “When we go ahead away from home like we did, we’ve got to do better as a group.
“To let four goals in during the second half is not good enough and we appreciate that.
“To say we were disappointed is an understatement. We prepare all week for games like this and to lose it hurt.
“To hear the Fulham boys go past in high spirits, it was a reality check for us and it was hard to sit and listen.
“We’ve got to take it on the chin, it was our own doing.
“We had the opportunity to win the game and we didn’t.
"We’ll put it to bed as soon as possible and look ahead to Saturday.”
Murray got back on the scoresheet for the first time since early December as he ended a eight-game goal drought in the league.
His double moved him on to ten Premier League goals, two short of the league total he managed last season, and he said: “It was nice to find the back of the net; I struggled with injuries and a bit of illness over Christmas, so to find the back of the net was a relief.
“I knew it would come eventually. I’ve learned not to worry about a drought because they do come eventually.”
Murray went close to a hat-trick and was denied by Fulham keeper Sergio Rico, at 2-0 and 3-2. Albion’s striker said: “They scored at key times and I felt their goalkeeper made a very good save from me at 2-2. Goals change games and if that had gone in, then the whole dynamic of the game would’ve changed.
“Unfortunately he made a fantastic save, they had the momentum and we couldn’t get our game going again.”
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