The Gunners were heading for an opening-day draw at the Emirates Stadium this evening until Ramsey struck in injury time to secure them a 2-1 victory.
"It was very difficult," the Wales international told Sky Sports News. "[Palace] came out and defended really well. It was very tough to break down.
"They lost their manager earlier on in the week but you'd never have known that the way they played today. But that's irrelevant, the result is what we were looking for and we got the three points.
"We found it difficult the first game of the season the last few years, so like I said it was important to get the three points today and we managed to do that so that's all that matters for us."
Arsenal are back in action on Tuesday night when they travel to face Besiktas in a Champions League qualifier.