The Hammers lost 2-1 at Stoke on Sunday, missing out on the chance of Wembley once again this season.
However, after back-to-back league victories, Avram Grant's men are now close to pulling out of the relegation zone.
Next up is a short trip to Champions League challengers Tottenham, where Tomkins hopes the Irons will show plenty of fighting spirit.
"We can't feel sorry for ourselves," the defender told the club`s official website. "The FA Cup would have been a bonus but the league is massively important, we have to bounce back.
"We have to put Stoke behind us and remember we were on a good run. We will be giving it everything at Tottenham."