Arsenal have lost back-to-back Premier League matches against Swansea City and Manchester United, and threw away a three-goal lead as they drew with Anderlecht last time out in the UEFA Champions League.
Wenger was openly criticised by billionaire shareholder Alisher Usmanov on Tuesday, but Ramsey says the 65-year-old has the full backing of the dressing room.
"With what he's done for this club and for us as a group of players, every time we go in we want to work for him and get results for him," Ramsey told Sky Sports News.
"Everybody's in it together, and we know all about our qualities.
"Last season we had a great year, this season we wanted to build on that and hopefully we still can.
"When you have a few bad results on the bounce a lot of things are being said, but it's important for us not to listen to that. It's important to stick together as a team.
"We know all about each other, we know what we have to do and now we just have to show it on the pitch."
Arsenal can reach the knockout stages of the Champions League for the 15th season in a row with a home draw against Borussia Dortmund on Wednesday.
