The Gunners lost 2-1 at Fulham on the back of disappointing 2-0 defeat to West Ham.
And Rice, 24, fired a warning to his team-mates after they fell to fourth in the Premier League table having led at Christmas.
He told Sky Sports: "Very disappointing, very tough to take, obviously not good enough. The last two results have not been what we've required or been setting over the course of the season.
"We've been performing well until the last two games, especially off the back of the draw at Liverpool, we felt like we could really kick on. But after the last two defeats, it's a tough one to swallow."
The Gunners were wasteful and struggled to close out the game today after Bukayo Saka's early opener.
Raul Jimenez levelled after the break and Bobby Decordova-Reid netted a second-half winner in what was a deserved result for the Cottagers.