Yesterday's 2-0 defeat at Heart of Midlothian put the Hoops ten points behind Old Firm rivals Rangers and even a point behind Motherwell in second and Matthews admits it is a precarious stage of the season for he and his teammates.
"If the gap gets any bigger, we've got no chance. We can't afford to lose another game," the Welsh full-back said.
"I think we now have to put a decent run together. Everyone at Celtic is under pressure - when you are at a club like this you expect success.
"But it's just not been the start we wanted and we're aware of it.
"We haven't hit our full potential, but we have good players and I am sure we can pull it back though.
"It was only when we went down to ten men today some heads dropped.
"Yes, there's a big gap, but we need to win our game in hand and kick on from there. We need to learn to win ugly.
"Rangers have that ability and we must do the same."