"I am willing to fight for my position and it is something I strive on. You have got to better yourself every time you go out onto the training field," the 26-year-old told the club's website.
"It was disappointing going out of the team after coming away with a good victory at the Emirates Stadium," he added.
"But it is all about showing what you can do in training and getting the performances in when you can. I want to stay in the team."
West Ham travel to Anfield, a venue where they have not won since 1963, to face Liverpool on Saturday and Tomkins is looking forward to facing major summer signing Christian Benteke after the Belgian completed a high-profile move from Aston Villa.
"He is a great striker and fully deserves his move. He is very good in the air and is a handful to play against at times," The England under-21 international said.
"Attacking wise they are very good and (Philippe) Coutinho has also been playing well.
"We will need to be wary all round the pitch but hopefully we will cause them problems as well," he added.
"I know people will say that the odds are against us after the last two games but no-one expected us to get a result like we did against Arsenal and hopefully we can do the same again."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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