The Welsh club took the lead after 15 minutes through Wilfried Bony, but Mile Jedinak stepped up to equalise from the spot after Marouane Chamakh had been brought down by Jonjo Shelvey.
Monk was disappointed with the manner of Palace's 25th-minute equaliser, but still found reason for satisfaction despite Swansea missing out on a third consecutive home win in the Premier League.
He said: "We started the game very, very much on the front foot. We got the goal and we were in the ascendancy and I'm disappointed really to have conceded that goal, purely from the point that it was the lead-up to that corner where we had given a sloppy ball away upfield.
"They countered and got the corner and obviously the goal came from there.
"That was disappointing but we had our chances. It was always going to be difficult. Palace defended well, I thought.
"Apart from the lead-up to the goal and three or four minutes after that, we controlled the whole game."
The 35-year old has courted controversy in recent weeks with his criticism of referees, and once again hinted that Swansea may have been hard done by.
Talking about the penalty decision, Monk added: "The footage that I've seen is pretty inconclusive.
"The referee [Martin Atkinson] gave the action that his [Chamakh's] legs had been taken away from him. From the footage I’ve seen there's no leg contact between the two players. It's more with the upper body, so I'm not too sure.
"But he's given it, we have to deal with that and move on."