Sinclair's £8m summer move to the Premier League champions opened the door for Routledge and he has taken full advantage.
"Everyone's frustrated when they are not playing," said Routledge, who looks to have finally settled after spells at Crystal Palace, Tottenham, Portsmouth, Fulham, Aston Villa, Cardiff, QPR and Newcastle.
"It doesn't matter who you are or where you are.
"Obviously I knew in the summer that Scott's move gave me a chance in the team.
"I have done that and it is going well. It is nice to be involved a bit more."