West Ham United have been the surprise package in the race for UEFA Champions League qualification this season and currently occupy sixth position in the Premier League table. David Moyes’ men have improved a lot this season, and the signing of Jesse Lingard seems to have spurred the team onto another level.However, West Ham face a tough battle against Leicester City, Chelsea, Liverpool and Tottenham Hotspur for a place in next season’s Champions League."It’s not over. Far from it. We’ve got three games to play and we’ll keep going for it."🗣 The boss' reaction following today's defeat...— West Ham United (@WestHam) May 9, 2021West Ham United suffer damaging defeat to EvertonWest Ham were on an impressive run between March and April but have now lost three of their last four league matches.On Sunday, they suffered yet another damaging defeat at the hands of Everton, allowing fourth-placed Chelsea to move six points clear of them.Among the teams competing for the Champions League spots, only the Hammers lost last week. Liverpool, Chelsea and Leicester City all won their respective games.Fortunately, West Ham have a game in hand and would be just three points behind the top-four places if they win. Another defeat, though, would be the final nail in their coffin."Everyone’s disappointed but we need to pick ourselves up because we’ve got another big game on the weekend."💬 @JesseLingard on bouncing back against Brighton...— West Ham United (@WestHam) May 10, 2021West Ham’s Champions League hopes fadeWest Ham’s hopes of qualifying for the Champions League suffered a huge blow when they lost to Chelsea last week.It appears the Hammers are yet to recover from that defeat. Their European hopes are still alive, but it is increasingly looking like they’ll end up in the Europa League.Moyes said after Sunday’s defeat to Everton (as quoted by Goal):"We want to keep going, we want to go right to the last day and see if we can sneak in [the Champions League. It will probably take us winning all of our games.""I think if we made European football this year it would be a brilliant achievement. I might admit I think I'd be disappointed now if we didn't get there, but I don't think it would change how we feel about the season and how we're doing."It has been a successful season for West Ham, irrespective of whether they qualify for the Champions League or not. The club seem to have overachieved already, but they’ll also be disappointed to miss out on a top-four place after putting up such a good fight.