The Cottagers were two up within the opening 35 minutes through a Dimitar Berbatov penalty and a Sascha Riether goal.
But Sunderland hit back through a Craig Gardner penalty and a Stephane Sessegnon effort with 20 minutes left to make the final score 2-2 in Saturday's Premier League clash at the Stadium of Light.
But Jol felt his side should have hung on for the win.
"I thought if you see the second half, you always expect something to happen but if you see the first half we dominated," said Jol - who felt Sunderland's penalty was harsh.
"The penalty situation was soft - there was a little bit of contact but not a lot and it gave them confidence and after it was not an easy second half, we should have scored and in hindsight we deserved a bit more."
Berbatov missed a great chance to win the match at 2-1 but Simon Mignolet saved and Sunderland broke and scored their equaliser.
"He also had a one-on-one with the keeper and that was disappointing," said Jol.
"They are a good side but they have not had a lot of wins at home so we know they play very adventurous and we dominated the midfield and I still feel we should have punished them."
Jol feels that nobody is yet safe towards the bottom of the table.
"Before today, if they had beat us they would have been on 32 - and everyone can be dragged into a difficult situation - on one hand a point is good but on the other three points would have meant we had done the business today but we didn't," he said.
Jol also paid tribute to Iranian Ashkan Dejagah, who was Fulham's best player.
"Dejagah is a marvellous player, but I want more goals and more assists and for him to be more productive and we saw that today," he added.
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