The Cottagers dominated for large periods of their clash at Craven Cottage and won the game thanks to second-half strikes from Bobby Zamora and Andy Johnson.
And although pleased with his side's efforts, Mowbray admitted Fulham were the better team.
"They thoroughly deserved to win," Mowbray admitted on Sky Sports.
"We rode our luck right from the start. We were better second half but lost goals through poor defending."
"We threatened their goal and if we had gone 1-0 up it might have been a different game but I can't stand here and say they didn't deserve the win.
"I think we could have scored goals, it was a big, big game and we tried to match them - it was a big ask and I am not going to stand here and criticise them."
Home formMowbray concedes that West Brom will be relying on their home form to stay up.
"At home we can question our team and ultimately that is where we are going to pick our points if we want to stay in this division," he said.
"We are going to try and win a game or two away from home of course, but that is football and as I said today Fulham deserved their win today."
The Baggies chief also insisted they were not about to change their approach to a more conservative one away from home.
"We play two up-front and still play the right way and we had enough shots on goal, we can make a good fist of it and we are giving ourselves a chance, the league is still tight and we have a good chance still," he said.
"Confidence is fine in the group, but any given day you have to keep going. You can always beat somebody if you have a goal threat."