Both sides lost ground in the battle for a Champions League place, but Cahill had no complaints about his side's performance.
Chelsea rested key players with the upcoming Champions League semi-final second leg against Barcelona. The Gunners dominated the majority of the game, hitting the woodwork twice through Robin van Persie and Laurent Koscielny.
"It was a good result and a good point for us," he told Sky Sports News.
"It was an early kick-off today and we only had a couple of days to rest up after the Barca game, but we did okay today, had one or two chances and they did as well so it was a fair result.
"Both defences were tight and it was cagey. We had one or two chances and perhaps the final ball on both teams lacked a bit, but a point is great result."
Chelsea remain sixth in the Premier League table with just four games remaining.