Leicester became just the second former Premier League champions to be relegated despite a 2-1 home victory over West Ham on the final day of the season.
David Moyes was relieved to come through a "difficult night" after West Ham recovered from a goal down to take a 2-1 lead into next week’s Europa Conference League second leg with AZ Alkmaar.
David De Gea's slip loosened Manchester United's grip on the final Champions League place as they were beaten 1-0 at West Ham.
Joel Matip's towering header saw Liverpool come from behind to beat West Ham 2-1 and pick up a third straight win.
David Moyes believes his West Ham players are ready to fight for their Premier League lives.
David Moyes is targeting another long run in Europe for West Ham after they put one foot in the quarter-finals of the Europa Conference League.