"At this stage of the season results are critical and we didn't concede any chances of note to let them score," Lampard told Sky Sports.
"Where we are at as a team and where we are in the table, it is all about the result.
Chelsea manager Frank Lampard: "They were better than us physically, in the mind and with the ball. So you lose the game. They were stronger than us. You feel and hear every noise and all I could hear was Sheffield United voices.
Lampard said as much himself when speaking to BBC Sport.
"There were moments in the game where our game-management wasn't great," said the Chelsea boss. "At 2-0 we can dominate that game and finish it.
"Pre-West Ham, we could have gone third and we let ourselves down," Lampard told Sky Sports.
"Today, there was a bit of pressure to get back to fourth and we produced - so get used to that pressure, whatever way it looks, because it's going to be tough all the way through.
West Ham boss David Moyes, speaking to BBC Sport:
On VAR decision: "At that moment I thought everything was going against us. The first goal is vital and when you lose it you think here we go again but great credit to the players, they kept at it and I thought we got the reward.
"I think we made Chelsea work very hard. It was always going to be a tough game for us - Chelsea are an established Champions League team," said Villa boss Smith
"We have worked all through the lockdown to be tougher to beat defensively and I thought we were.
Chelsea manager Frank Lampard: "We have injuries but that gives opportunity so we don't want to moan, especially when Billy Gilmour plays how he plays, and Ross Barkley and Mason Mount, and the collective of the team.
"The last five performances have been stronger and we've started to score goals and create chances from open play," said Howe.
"We're not where we want to be though, and it's going to be really tight and a big battle to get the points we need from now until the end of the season.