Everton boss Frank Lampard said his side need to show "more quality" to avoid Premier League relegation but remained confident they would stay up.
The Toffees, 17th in the table, lost 2-1 at West Ham and are only three points above the relegation zone before facing 19th-placed Burnley away on Wednesday.
"We're in this position and know the reality but we have 10 games and a lot of points to fight for," said Lampard.
"If we keep on the path we showed I have a strong belief we will be OK."
West Ham went ahead through Aaron Cresswell's superb first-half free-kick before Mason Holgate equalised early in the second half.
However, Everton, whose total of six away points is the lowest of any of the 92 sides in the Premier League or EFL, fell behind again five minutes later to Jarrod Bowen's winning goal.
"We have to show more quality - and there is that in this group - to stay up," added Lampard after his side lost for the sixth time in eight league matches since he replaced the sacked Rafael Benitez in January.
"Everton has huge history and a fanbase. At the moment we're working to get through this moment. Myself and the players are giving everything. The fans can know if we keep doing that over 10 games we will be OK."
'Everton have quality in areas other clubs don't have'
Everton have played in English football's top flight every year since 1954-55 and Hammers boss David Moyes, in charge of the Toffees for 11 years between 2002 and 2013, expects his old club to maintain that record.
"I think Everton will be OK when they have the quality of players they have with a Brazil centre-forward (Richarlison) and an England centre-forward (Dominic Calvert-Lewin)," said Moyes.
"Everton have got good things going for them and should feel more positive. It's not a good place to be and you never know how it's going to go but Everton have quality in some areas that other clubs don't have."
However, former England defender Jonathan Woodgate, speaking on BBC Radio 5 Live, felt the Everton players needed to work harder to ensure their safety.
"When Everton lose the ball, the five that are forward don't get back in time, they don't bust a gut to get back and start defending," said Woodgate.
"If you look at how easily they are being played through, there's been no real heart, no real fight, no desire to really make the difference.
"You can't always look at the managers. Sometimes the buck has to stop with the players."
Moyes repeats call for Bowen to get England recognition
Uncapped Bowen had been tipped for an England call-up for the friendlies against Switzerland and Ivory Coast last month before a fractured foot ended those hopes.
However, Moyes felt the 25-year-old forward, who has now scored 13 goals in all competitions this season, could make a late push to get into Gareth Southgate's squad for four Nations League games in June - against Hungary, Germany, Italy and Hungary again - and the Qatar World Cup in November and December.
"It was unfortunate the injury he got as we could have found him being part of the England squad," said Moyes.
"Gareth may look at him again in the summer if he keeps his form up. We know Jarrod has goals in him.
"He has such high standards and he might've been called up for England in the last break. If he finishes the season well he will be in contention for the games in June."
For Moyes, his thoughts now turn to Thursday's Europa League quarter-final first leg when they take on French side Lyon at London Stadium with Barcelona potential opponents in the semi-finals.
"This is just the starter," added the Hammers boss. "We have the main course coming up on Thursday and hopefully we can be quicker and sharper."
West Ham have only won one European competition in their history in 1965 and have never played in the Champions League, but winning the Europa League would guarantee them a place in that competition next year.
Sunday's win leaves them sixth in the Premier League on 51 points, three behind fourth-placed Tottenham, who beat Newcastle 5-1 later in the day. Spurs have a game in hand while fifth-placed Arsenal - also on 54 points - have three games in hand on the Hammers.
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