Portugal forward Orlando Sa had netted after just six minutes to put the visitors on course for a rare away win.
Norwich, though, continued to press and deep into five minutes of stoppage time, Canada striker Jackson nodded in Elliott Bennett's right wing cross.
Lambert felt the final result was nothing more than his battling side deserved.
"I thought it was no more than we deserved, especially in the second half, when we were relentless at times," the Norwich manager said.
"We played in fits and starts in the first half against a really good side, people underestimate Fulham, but in the second half we were very good.
"The crowd were a bit flat and expecting us just to win, which I think is wrong, the lads have given everything and the players need the crowd to help them along.
"In the second half, the lads dragged it up by themselves and were excellent.
"The crowd have to realise we have to manage the expectancy level.
"The early goal put us on the back foot, but the lads keep going, have got a great desire and it is all credit to them, because their effort was extraordinary."
Norwich moved back into the top 10 to end what has been a positive first half of the season on their return to the Barclays Premier League ahead of the trip to Queen's Park Rangers on January 2.
Lambert hopes to bring in some fresh faces next month, but admits there can be few complaints about the current group's progress this year.
"I am delighted with the effort and where we are sitting, as I have said before that people would have put us in the bottom three at this time of year," said the Norwich manager.
"I have nothing but admiration for the players, they have been colossal for me."
Lambert revealed he would like to make full-back Kyle Naughton's loan move from Tottenham permanent if possible.
He said: "With the way he has played, we would like it to happen. Hopefully it will be tied up and I will probably speak to [Spurs] manager Harry [Redknapp] really soon."
Fulham could have easily taken more control of the match, with Clint Dempsey's first half header coming back off the bar.
However, once front duo Sa and Kerim Frei had come off for the closing stages, the visitors lost their attacking outlet.
Cottagers boss Martin Jol was disappointed his team could not close the match out during five minutes of stoppage time.
"We were sitting a bit deep and could not get out of our half any more, but we had defended well, and you always hope to keep it like that," Jol said.
"In the first half, we were the better team, but we could have scored the second goal, which is disappointing.
"You always know they are capable with their style of getting a goal."
Jol added: "We look dangerous and had a few chances, but we needed a cushion - two goals would probably have been the end of it.
"The way we defended the second half was good, but maybe were a bit deep, had a few tired legs, and then it is only a matter of them nicking the ball."