The Clarets remain seventh in the standings, with 34 points from 23 games, but have not win since beating Stoke City 1-0 on December 12.
"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.
"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".
Palace have now suffered just one defeat in their last 12 league matches and while there will still be some moments of anxiety, mainly in the closing stages as another priceless win was so tantalisingly close, this was another performance to warm the hearts of the South London faithful.
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"You look at that, a couple of decisions have gone against us in this run, a few injuries, so I'm not overly disappointed".
The Burnley star has featured 15 times in the league this campaign as the Lancashire club have defied the odds to now reside in the top half of the table. "But we make it clear to anyone who comes here, whether they are signings or loans, that they have got to earn the right to play".
The Red Devils are now overstocked in the positions Fosu-Mensah would normally be considered to play in and so he was sent out on loan to another Premier League club to learn his trade.
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"I have a very positive feeling about our group of players, we have a talented squad, as our results have shown, so I think we will continue to do well but we have to be on it every week".
"It was a close-but-no-cigar afternoon", Dyche said. "We started to really try and be more productive than we were first half".
"Second half, we were at least decent and thought we probably deserved to scratch a draw out of the game in the end".
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Despite his win, England's Casey said his opponents fought hard: "What great golf we played, but the Asians threw a lot at us".