A first-half strike from Morgan Amalfitano was enough to gift the Baggies victory at Carrow Road as they leapfrogged their way in 16th in the Premier League standings.
Defeat leaves Norwich hanging precariously close to the relegation zone, with only five points separating them from the dreaded drop-zone.
Hughton's side face 18th-placed Fulham next weekend before ending their season against Chelsea, Manchester United, Liverpool and Arsenal.
"It does put pressure on us," Hughton told Sky Sports.
"But we've done this ourselves. We could have alleviated that with a win today but we knew that before today.
"We knew our away form has been poor and we have to be able to produce in the home games, which we generally have done.
"But in the last couple of games we haven't been able to do that, it's a tough one to take today because our performance wasn't good enough."
After the full-time whistle, yellow clap-banners - provided to encourage fans to get behind the home team - were thrown in the direction of Hughton and his players and the manager is willing to accept responsibility for the defeat.
"I'm aware of that," he said when quizzed on the fans' display of upset.
"It's been a bad day for us and our supporters will react to what they see on the football pitch.
"I will never accuse my players of not showing enough endeavour or not being desperate enough to win the game, but we didn't have enough quality today.
"I expect to take any criticisms from the performance today, I very much accept that and you have to."
Amalfitano broke the deadlock on 16 minutes before West Brom sat back to protect their lead and Hughton believes Norwich failed to seize their opportunities.
"We conceded a poor goal which allowed a good West Brom side to sit back and allow us to make the play," he added.
"They played very well on the counter attack, they probably had one clear chance but it was a soft goal that we conceded.
"We didn't make the most of the possession we had and we didn't get into the areas we needed to."
Hughton understands the ramifications of defeat to West Brom but admits his side fell short in performance levels.
"Do I think we deserved to lose the game? No I don't," he claimed.
"But we're at home. At home against a team that are around us in this division and we have to do more to win it."
Norwich's best chances of the match came in the second half as Gary Hooper and Robert Snodgrass both rattled the woodwork and Hughton applauded the resilient West Brom defence.
"They were tight as a unit and you have to show that bit of quality in the final third to create better chances than what we had.
"I know we hit the woodwork on two occasions and I know we threatened a lot but really didn't create good enough chances.
"We never really tested the keeper enough, you can't concede a soft goal and we needed to show more in the final third."