Snodgrass, 31, made 33 appearances including 25 starts for the Hammers last season, scoring a couple of goals as the East End outfit finished 10th in the standings.
However, the Scotland international has started just once in the league in the early part of 2019-2020, with two further appearances off the bench as West Ham sit seventh in the table after four games.
The former Hull City man is currently on international duty as the Scots prepare to face Russia and Belgium in a couple of Euro 2020 qualifiers, and he will hope to see more game time when returning to club action later this month.
However, with the London Stadium outfit enjoying such a good start in the Premier League, it is unlikely that Pellegrini will change too much and Snodgrass is happy to bide his time and lend his support to those who do make the starting XI.
"If you're not playing me, just be honest with me. I'm fine with that," he told the Glasgow Evening Times. "I'm going through that state at West Ham just now.
"When that happens you need to be a good team-mate. If you have a team full of boys like that you'll go further."
West Ham are on a run of three consecutive wins, having beaten Watford and Norwich City in the league while taking care of Newport County 2-0 in the Carabao Cup.
With pressure mounting on Pellegrini after a poor season in 2018-19, he has responded well with some decent new additions to the squad during the summer months.
Snodgrass, who signed in January 2017, is one of the senior figures at the club and his words of support will only help forge an even better team spirit within the ranks.