A late Cheikhou Kouyate goal secured a point against the Canaries during a 2-2 draw.
Goals from Robbie Brady and Nathan Redmond had both given the Canaries the lead at different stages in the game, with Diafra Sakho having drawn the scores level the first time and Cheikhou Kouyate netting a late equaliser to rescue a point.
It was another disappointing home result for the Hammers, whose Upton Park form is in stark contrast to their so far imperious away form, and Tomkins admits there was a sense of relief that they secured a late point.
"We're relieved to come away with a point. They put us under a lot of pressure towards the end of the second half," he told whufc.com.
"They started a lot brighter than us too and got their goals, so we're quite happy to come away with a point even though we obviously wanted three points at the start of the game."
"Anyone can beat anyone in the Premier League"
It was another disappointing result for Slaven Bilic’s side at home, with them so far having won just once at Upton Park this season, losing to Bournemouth and Leicester and only beating struggling Newcastle United.
That is, of course, in stark contrast to their away form, where they have managed to beat the likes of Arsenal, Liverpool and Manchester City so far in this campaign.
That is likely to be frustrating for Bilic and his West Ham side, who currently sit third in the Premier League table, but Tomkins says it just goes to show anyone can beat anyone in the Premier League.
"We're just taking each game as it comes," he added.
"We've done exceptionally well against the big dogs away from home but at home against the teams not in that category it's shown that anyone can beat anyone in the Premier League."