Jewell said: "I am delighted with the result and our second-half performance, but disappointed with the first half when we were very poor.
"I lost my temper with my players at half-time but it seemed to work as we were much stronger than Cardiff in the second half.
"We have overcome a poor start to the game to win but we have to believe we can compete at this level.
"We sat off Cardiff in the first half and it looked as though we were expecting to lose so half-time came at the right moment."
He added: "Jimmy Bullard struck two great goals but in the second half we looked to break quickly and he seemed to run the game in the final 20 minutes or so.
"This is a tough place to come and our goalkeeper has kept us in it with a superb display."
Arsenal loanee Jay Emmanuel-Thomas was denied by Fulop on three occasions as well as Peter Whittingham and Michael Chopra.
Whittingham also saw his free-kick hit the crossbar while centre-back Dekel Keinan's first-half header was ruled out for offside.
And Cardiff assistant manager Terry Burton could not be too downhearted about the display but felt it definitely amounted to points dropped as they passed up on the chance to leapfrog rivals Swansea into second place in the table.
"It was a great opportunity missed and we are disappointed, but the performance did not warrant a 2-0 defeat," he said.
"We had created chances and had a legitimate goal disallowed at a time when we were running the game.
"Their goalkeeper got lucky but that's his job. After they scored they had something to cling on to and we were left chasing the game but you have to put your chances away when they come.
"The performance, by and large, was decent but we can get better and it is not very often you are so on top in one half yet end up losing the game.
"There are still 33 points to win and I wouldn't like to guess who will end up in the top two, but I cannot understand how some officials give us very few decisions even when they look so clear-cut."