David Moyes says it "nearly feels uneasy" talking about West Ham's place near the top of the Premier League after the Hammers beat bottom club Sheffield United.
Declan Rice's penalty, a header by Issa Diop and a third from substitute Ryan Fredericks lifted Moyes' side into the top four and a Champions League spot.
However, Chelsea's win over Newcastle in Monday's late kick-off meant West Ham finished the day fifth - above champions Liverpool.
"We've got five games before April and if we make it to there it might start hotting up," said Moyes after a sixth West Ham win in eight league games.
"But it nearly feels uneasy talking like this. The teams around us are top, top teams and we are going to have to play incredibly well to be there.
"But I think we've got another gear or two to what we've shown tonight."
Chris Basham's lunge on Jesse Lingard helped gift the Hammers victory, Rice making no mistake from the spot before Diop, who was forced off with a head injury in his previous game, doubled the lead from Aaron Cresswell's corner.
Substitute Fredericks added a third deep into stoppage time.
Sheffield United, 14 points from safety with 14 games left, went close to equalizing at 1-0 only for Lukasz Fabianski to produce an outstanding save to keep out David McGoldrick's deflected header.
