Victory saw the Baggies overtake Norwich in the Premier League standings on goal difference, meaning they are now five points above the dreaded relegation zone.
Albion also boast a game in hand on a number of surrounding teams, but Foster was quick to highlight fixtures against Manchester City, Tottenham and Arsenal.
After a 95th-minute Cardiff equaliser snatched two points from West Brom last weekend, Foster hailed a fantastic response from his side.
"It was a monster win for us today," he told Sky Sports.
"We've got seven games left and we have a couple of tough ones in there, we've got to play City, Tottenham and Arsenal as well.
"The teams around us we're playing it's important to pick up three points.
"We started today, it was a fantastic response from the lads after last week and we're really, really happy."
After taking the lead inside 16 minutes, West Brom turned attention to defence and Foster was full of praise for head coach Pepe Mel and his assistant Keith Downing.
"I have to say a massive well done to the management staff really," he added.
"Keith and Pepe have been great. We were more than happy to let them have it at the back but when it came into the midfield, our midfield were on them, they worked like dogs all day.
"Fair play to them. They're absolutely knackered now but any tiredness goes when we see those three points on the table."
Albion players raced to celebrate with Mel at the full-time whistle and Foster admits the Spanish coach has endeared himself to the West Brom dressing room.
"You could see him on the pitch at the end, getting absolutely bombarded by the lads," he recalled.
"They'll probably be jumping all over him in the dressing room, he's a lovely guy.
"You can see how much it means to him and we will revel in that too. When you're down there and it gets nervy, you have to dig in and we did that today."