The Clarets remain seventh in the standings, with 34 points from 23 games, but have not win since beating Stoke City 1-0 on Dec. 12.
Their position is still an improvement on the same stage of last season, when they were three places and five points worse off.
"The margins were tight early-season when we were winning a lot of games and the margins are tight now," Dyche told a news conference. "I still think we have moved a long way from where we were last season, particularly away from home, because second half, we have really taken that game on today.
"It's a bit of a tough run at the minute, but over the course of the season, it's a hard one to judge. Before this run, we had just won three out of four and were unlucky in the one that we didn't win.
"You look at that, a couple of decisions have gone against us in this run, a few injuries, so I'm not overly disappointed. I'm certainly not disappointed by the look at the league table."
Dyche said a possible reason for Burnley's current slump is that they have been slow to get going in matches.
"Early season we were making victories our own," he added.
"Now, we have to make them come our way. No one in the Premier League waits for it to happen, and I thought first half (against Palace) we were playing a bit like that. The Premier League is just not like that."
Palace went ahead through Bakary Sako's 21st-minute strike, although Burnley forwards Sam Vokes and Ashley Barnes both spurned two chances apiece to equalise.
"It was a close-but-no-cigar afternoon," Dyche said. "They were better than us in the first half, not by miles.
"Second half, we were at least decent and thought we probably deserved to scratch a draw out of the game in the end."
(Reporting by Matt Westby; Editing by Christian Radnedge)
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