Sunderland - Roberto Martinez believes his Everton squad have the character and ability to stay in the mix for a Champions League place after achieving a club record points total in the Premier League era.
The Merseyside team climbed up to fourth spot with a narrow 1-0 win away to Sunderland, a seventh consecutive victory moving them on to 66 points, bettering their previous best under former manager David Moyes in 2008.
Now Martinez wants to see his players maintain their momentum ahead of back-to-back homes games with Crystal Palace and Moyes's Manchester United, fixtures which will go a long way to deciding their top four ambitions.
"We're fighting to achieve something but there's no pressure because at the start of the season we weren't among the top six favourites," said Martinez.
"It's hard to say how many points will seal fourth but it will probably be the highest in Premier League history," the Spaniard added.
"Our objective is to stay fourth. We're going into new ground with the highest Premier League points tally. We're taking every game with real excitement.
"Players are desperate to play and compete for places. To have 66 points by this stage is very good."
An own-goal from Sunderland defender Wes Brown in the 75th minute proved the deciding factor in a tight affair at the Stadium of Light.
Brown's frustration, which saw him turn a Gerard Deulofeu cross beyond goalkeeper Vito Mannone, heightened bottom of the table Sunderland's relegation concerns but increased Everton's hopes of sealing a Champions League spot in Martinez's first season in charge.
The former Wigan manager added: "The winning goal was reward for the way we kept going forward. I felt it was a bit of magic to get something out of nothing and that's what Gerard did. He was very sharp and every time he got into the 18 yard box he was a real clear threat."
Sunderland, however, are left staring at a seven-point gap to safety with time running out.
Black Cats boss Gus Poyet thought it no coincidence that Brown's goal was the sixth time this season a Sunderland player had scored in his own net in the Premier League.
"Something always happens and it hurts because it doesn't matter what we do, it happens," said Poyet. "That's not an excuse. I don't really believe in luck, being lucky.
"It's true that if you are at the top you can get something which goes for you, when you are the bottom it doesn't. It's another own-goal and that's too many in one season," the Uruguayan added.
"When you play like that you always have a chance. But we are running out of games and we need to make sure that changes quickly.
"As you know, the next two games (against Manchester City and Chelsea) are more difficult because of the quality of the opposition."
Martinez, meanwhile, praised the majority of the crowd at the Stadium of Light for respecting the minute's silence held as a tribute to the 96 Liverpool fans who lost their lives in the Hillsborough disaster 25 years ago.
There were interruptions from a few supporters, but Martinez, the manager of Liverpool-based Everton, said: "It was people entering the ground and they weren't aware it was the minute's silence.
"The silence in the ground was full of respect."