The forward arrived at Firhill earlier this summer after a difficult spell at Hearts that saw him become one of the elder statesmen in the Tynecastle dressing room during the club's financial troubles.
Stevenson netted his first Thistle goal in the 1-1 draw with Dumbarton on Saturday and is happy to pass on his top-flight nous to his new team-mates as they prepare for their second season in the SPFL Premiership.
He said: "I put the responsibility on myself to do well and try and help others do well.
"I have had it for the last couple of years at Hearts and sort of grown into that position now. I don't really ever see it leaving me. I am getting older and I am here to help the boys.
"If I can pass on experience of situations that I have been in to the boys then I will do that, the same as they will with me.
"It is fresh for me. The fans will help me as well. You always want to do better than what you did the previous year.
"It is a big club and the pressure will be put on by ourselves. We want to do well and finish as high up as we can.
"It is so open and there is no reason why we can't."
Thistle will continue their preparations for the new season with a friendly against Glentoran this weekend but face an extra few days wait to begin their Premiership campaign next month.
The visit of Ross County on August 13 will be their first game as their opening weekend clash with champions Celtic was postponed.
And Stevenson admits it will be a strange start for the Firhill side.
He said: "It is not ideal. When you see the fixtures coming out and you see the opening weekend, it is a big weekend and something you build up to during the pre-season.
"We are going to have to wait until the Wednesday night and that is just the way it is.
"We will look forward to it. It might be nice to sit back and see some of the teams or maybe even catch a game.
"It is a bit frustrating but we will look forward to the Wednesday night and, me personally, to playing my first competitive game for Partick."