The Baggies chief bemoaned his own strikers as the Clarets claimed a 3-1 victory at Turf Moor to move into the fifth round.
Gianni Zuiverloon had given West Brom some hope with his goal after Wade Elliott and Steve Thompson scored.
But the Baggies could not find the equaliser as Thompson scored the third late on and Mowbray admits Burnley deserved to go through as they took their chances.
"Let's sit here and give Burnley great credit," said Mowbray.
"They worked extremely hard, they got the goals, they have gone through to the next round and we wish them well.
"We missed a couple of good chances and found ourselves down to a great strike, but good luck to Burnley, we missed a few chances but so did they.
"They have some good players, and I felt tonight we were pretty comfortable and thought we were the better side and yet that doesn't matter, football is about putting the ball in the net.
"I thought their strikers showed great quality and desire in the last third, which out strikers lacked and I that is something that has been around us all season really, we have not been as clinical as we need to be."
Mowbray revealed that Jay Simpson had a hamstring issue which forced him off midway through the first half.
"Looks like he has got a slight strain on his hamstring and it doesn't help the cause, but we have to deal with it," he added.
The Baggies chief is also considering what to do with deadline day signing Juan Carlos Menseguez.
"We will see how he adapts, he is a bit of a wild card for us coming from South American football," he said.
"When the opportunity comes to give him time on the pitch we will, he is something a little different, a wide player with some tricks and a bit of individuality and lets see if he gets the opportunity to play."
Coyle delightBurnley chief Owen Coyle was quick to hail his side after they beat yet another Premier League side.
West Brom are the latest side to be beaten by the Clarets after Fulham, Arsenal and Chelsea all fell to the Championship club in the Carling Cup.
He said: "It was probably the best, as it is the one that counts now - the Carling Cup is finished, it was great while we were on it but we would love to have an FA Cup adventure similar to that.
"Each game we want to win, we were underdogs again against a Premier League side and we knew it was going to be a hard game, but it was a good footballing game with two teams trying to play football. I thought we deserved the win and being underdogs it is always good to beat a Premier League side.
"I am not going to pick out individuals as each and every one of them to the man gave everything they had.
"The way we went about it is what I want as a manager."
Coyle's side will now face Arsenal or Cardiff, and he admitted he doesn't have a preference - but insists they have a great chance against either side.
"We can't rule Cardiff out, it is not a 'gimme' - whoever we play, it is away but whoever it is it will be a tough tie, but it is a chance to get into the quarter-finals," he continued.
"We know when we can get to that level we can win matches, and we have shown that both home and away and wherever we go we will be positive as I insist to my players whenever we play."