The Hammers have produced a 0-0 draw with Chelsea, a 2-0 victory over Swansea City and a 2-0 triumph at Aston Villa in their past three outings to now sit 15th on the table and two points clear of the bottom three.
However, Tomkins says that is no reason to rest as the east Londoners get set to host 16th-placed Norwich City on Tuesday night.
"It is certainly not the time to sit back," he told the Newham Recorder.
"We need to carry on from the win against West Ham because we all know if you lose a couple of games, you are dragged right into the trouble again.
"We are hoping to keep this run going and Norwich is a winnable game, no disrespect to them, but it is a game we can win.
"The lads are so confident at the minute. We won our last home game and don't forget about the Chelsea game which was massive as well, and then beating Villa, so we are confident going into Tuesday, but we will need our whole squad because there are likely to be some tired legs after the Villa match."
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