Midfielder Cheikhou Kouyate knows West Ham cannot allow their work-rate to drop if they are to build on a positive start to the Barclays Premier League season.
The Irons were seconds away from suffering a third home defeat in four league games when they trailed Norwich 2-1 deep into stoppage time.
However, a free-kick from Dimitri Payet resulted in a scramble in the six-yard box following John Ruddy's deflected punch-out before Kouyate lashed the loose ball home as Upton Park erupted.
Slaven Bilic's men remain in third place, above Arsenal on goal difference.
West Ham have two away matches next, at struggling Sunderland and then London rivals Crystal Palace, where they will look to follow on from victories at the Emirates Stadium, Anfield and Manchester City.
Bilic highlighted the need for his players to match the energy of teams like Norwich, who had taken an early lead through Robbie Blake before Diafra Sakho levelled and then looked to have snatched a late winner following a fine strike by substitute Nathan Redmond.
It is an approach Senegal international Kouyate wants everyone to take on board.
"All the players wanted to win the game, but it was a very difficult game. Norwich played well and with very good organisation," Kouyate said on West Ham TV.
"Third (place) is not bad. We just need to keep working hard.
"We need to stay humble, work hard and go to Sunderland to battle for the points.
"I know Sunderland have not had good results (so far this season), but this is a very dangerous match."
Norwich, who had not won at the Boleyn Ground since 1989, are now unbeaten in three Premier League matches as they aim to re-establish themselves back in the top flight having come up through the play-offs.
With on loan West Ham winger Matt Jarvis not available, Norwich manager Alex Neil rejigged his starting XI at Upton Park, pushing Brady into a more attacking role on the left in front of Sweden international Martin Olsson.
The 23-year-old Republic of Ireland international, a summer signing from Hull, made the most of his opportunity, latching onto a stray pass from Irons skipper Mark Noble to put Norwich ahead on nine minutes.
While the Canaries were disappointed not to have been able to hold on following Redmond's fine strike with just seven minutes left, Brady is confident they have enough to compete at this level.
"It keeps our good run going, but it is frustrating at the same time," Brady told Norwich City TV.
"It is obviously good to take a point from places like this and Anfield (last week). Hopefully we can keep picking up results to get ourselves safe.
"The lads were excellent, so if we can iron out the mistakes then we will be fine."