David Silva scored twice for the hosts, while Steve Sidwell struck the post for the Cottagers. That near-miss aside, the visitors created very few chances but they did frustrate City for periods with their patient play and manager Jol felt they could have sneaked a result.
He said: "You are fearful - we were very concerned because if you concede a goal after one-and-a-half minutes, you really fear for a bad game, a bad afternoon. But it wasn't, we did okay. If you consider they scored the second goal in the 69th minute, we could have hurt them.
"In the first half they had a shot from (Edin) Dzeko over the bar and a shot from (Carlos) Tevez but that was probably it. I felt we could have done a bit more and scored the equaliser. But if you have got Silva - he has extra quality, probably the best player in the Premier League. He was fantastic but overall I felt we did okay."
Left-back John Arne Riise was again left out of the Fulham side but Jol, days after denying he had fallen out with the player, was quick to quash rumours the Norwegian had refused to travel.
Jol, however, did confirm that his absence was related to a poor performance in the 4-0 thrashing by his former club Liverpool before Christmas.
Jol said: "John Arne Riise is a fantastic boy - he will never come up with that sort of c p, he didn't want to travel.
"If you have got (Matthew) Briggs, who is younger and who can go on the bench - John Arne Riise stayed at Motspur Park to do an extra session.
"I promised him if he was not starting it is probably better if you don't go with us. I wasn't happy after the Liverpool game, when (Stewart) Downing scored his first goal since joining Liverpool - John was playing against him, and there was another goal.
"I am trying to do something, maybe to freshen things up or alert John to do more or to do better. He is an experienced player, so if he is not playing he is not happy. He wants to play but I have got three left-backs now. Keiran (Richardson) probably did the best job of the three."