The Premier League outfit lost the third qualifying round 4-3 on aggregate to Romanian side Astra Giurgiu.
Having drawn the first leg of the tie 2-2 at the Boleyn Ground last week, the Hammers lost the second leg 2-1 away from home on Thursday.
Lee, who started Thursday’s second leg and played for 80 minutes, has taken to Twitter to express his disappointment.
We are all disappointed with our early ending run in Europe League,but now we need to be united,strong & focused on sunday game! Go Hammers— Adrián San Miguel (@AdriSanMiguel) August 6, 2015
Failure to play in the Europa League proper will be a huge disappointment to West Ham, but it is time that they turn their focus to the Premier League.
The first league game of the season for the Hammers is against Arsenal away from home at the Emirates Stadium on Sunday.