Since the start of the 2008-09 season the Toffees have won just five of 65 matches, losing 37, against Liverpool, Manchester United, Manchester City, Arsenal, Chelsea and Sunday's opponents Tottenham.
Their last victory against one of that group was in January 2017 when they surprisingly beat Manchester City 4-0 at home.
A succession of managers have tried various approaches to reduce the gulf and this season, with United's struggles under Jose Mourinho before he was sacked representing their best opportunity in a while to break into the top six.
They are only two points behind the sixth-placed Red Devils heading into the weekend but Silva admits it is likely to be a long process as the spending power of the big six will always represent a significant hurdle.
"In terms of money, when you look to their wages there is a big difference to what some of them pay and what we do but that is part of the game," he said.
"We have to work with our players, getting stronger every day, and give them the conditions to play stronger against these type of teams because we have enough quality, in my opinion, and confidence to try to beat them.
"It is something we are working on. It is not something you achieve easily or fast. Our fans want it tomorrow and for the next match.
"I know the record, I know all these numbers. About closing the gap it is something which we are working to achieve, which is not easy.
"It is not just what we want, other clubs want it as well."
After five away matches against the top six Sunday will be their first home fixture against one of that group.
A goalless draw at Chelsea and an added time 1-0 defeat at Liverpool have given Silva optimism his team, who have yet to beat a top eight side this season, can get a result over the line.
"Of course we didn't achieve the good results for us in the last five matches against them," added the Portuguese.
"We have to be more effective, because we keep creating chances. Even in the last game against City (a 3-1 defeat) we created enough chances to achieve a different result.
"Of course, even if you don't score if you keep solid and compact and don't give chances to score you are always close to winning the match.
"We have to work hard as a team. It (Sunday) will be a tough match against a very good team, not just with individual quality but collective quality too.
"They have a very good manager. They are doing fantastic work, they are really close to the first two positions in the table.
"It will be the first game at home against one of the top six this season and it will be a good opportunity for us to show our quality.
"We have all the confidence to play our game and do everything to win the game and show we are able to beat them.
"We already showed enough capacity to play against these types of teams: in some moments we missed something but I hope we learn from these situations and can win the match."
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