The draw moved both teams up the standings by one position, with Palace rising to eighth place on eight points from six games, the same as Fulham in ninth.
Fulham edged an entertaining first half, which had significantly more cynical fouls and crunching tackles than clear-cut opportunities.
"I felt good -- there were a couple of saves in there," Johnstone said. "It is nice to do that and to get a point but it would have been better with three."
With manager Roy Hodgson back on the touchline after missing last week's
to Aston Villa due to illness, Palace weathered the storm and grew into the contest.
Eberechi Eze came close to scoring for the hosts in the first half, sending a curling shot just wide of the post from the edge of the penalty area in the 42nd minute.
Palace caused Fulham more problems in the second half, with Eze emerging as their standout player in attack as he had two penalty claims denied and kept the opposition defence on their toes with his skill and speed.
Fulham striker Raul Jimenez was unable to bring an end to his quest for a first goal since moving to London from Wolverhampton Wanderers in the summer, twice failing to score from promising opportunities before being taken off in the 79th minute for Carlos Vinicius.
In an end-to-end closing spell, Willian and Palace substitute Jean-Philippe Mateta both had chances to score from counter-attacks but neither player was able to break the deadlock.
"(A draw) is a fair reflection, really," added Johnstone. "We had some good chances, they had some good chances.
"Premier League games are never easy so I think it's a fair result. You never know what can happen on matchday."
The clean sheet was Fulham's third in six matches, this season's joint-best record along with leaders and defending champions Manchester City.
Both teams are next in action in the League Cup, with Fulham hosting Norwich on Wednesday and Palace travelling to Manchester United on Tuesday.
- Paul Tierney
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