Actually, several saints (e.g. St. Ignatii Brianchaninov) say that praying the Jesus Prayer during services can actually help us concentrate on the services better, especially when the services are very long.
I certainly find that using a komboschini during services often helps me focus, not just on prayer in general, but on the words being said. I know many priests who use one while serving the Liturgy, so it needn't be an either or thing.
Also, many of us attend parishes where large parts of the services are in a language we don't understand. Sometimes the music in some churches even makes it difficult to understand things sung in a language you do
speak. This is not a problem when it comes to the fixed parts of the service, but during the variable stuff a komboschini can be a great help in preventing you from drifting off.