The Merseyside outfit moved within three points of the Champions League places after their comfortable 2-0 win over Queens Park Rangers on Saturday.
Distin has said that his side are looking to finish as high as possible in the Premier League table after their recent run of fine form.
"It will be a great achievement if we do secure Europe because we don't have a massive squad," the Frenchman told Press Association Sport.
"We know financially we are not in position to buy four or five players every transfer window but we still compete against teams who spend 10 or even 100 times more than we do.
"From that point of view that is great but at the same time if we qualify for the Europa League or at best Champions League we have a small squad so we might suffer from it and only time will tell. All we want is to finish as high as possible."
The Toffees are currently in sixth place in the table.