The Spanish outfit clinched a record fourth Europa League crown on Wednesday with a 3-2 victory over Dnipro in Warsaw, successfully defending the title they won with victory over Benfica in Turin 12 months ago.
And the consistent successes have led to interest in Emery from the likes of AC Milan, Real Madrid and West Ham United in recent weeks, but Carrico is hopeful that the players will be able to persuade him to stay now that Champions League football has been secured.
"I think he is the key for us. He is our leader, a very important coach. We hope he will stay with us for next season but it is difficult because he is one of the best coaches in the world," Carrico told Goal.
"But now that we are going to play in the Champions League I hope that will help to persuade him to stay with us.
"We will beg him to stay. Of course nobody can ask more than to play in the Champions League. We are going to play in the best competition and that might help us when we ask him to stay."
The Rojiblancos were backed by around 10,000 in the Stadion Narodowy, and Carrico was quick to praise their impact throughout a season which also saw them finish in fifth place in La Liga.
"The fans are crazy. You should see at least one game in our stadium because it is unbelievable how they help us to win games. Sometimes we are losing and when they start to sing it is unbelievable. We just keep winning for them.
"We went 34 games one year without losing a game in our stadium, and in that you can see how important our supporters are."
And with Champions League football to come, the 26-year-old says there is no reason why they cannot succeed in the showpiece competition.
"We don't know what more we can do, but we have great ambitions and next season we will play in the Champions League. It's the biggest competition in the world and we want to do something in this competition."
