The Fifers have been taking huge strides in recent weeks as they worked to claw back the points deficit to those above them.
That deficit was reduced to just three points last week thanks to a magnificent 2-0 win over ninth placed Dumbarton.
And with Sons entertaining Falkirk at the weekend, there was a chance for East Fife to go neck and neck with Stevie Farrell’s side.
To do that, though, they had to beat the Bully Wee on their home match.
Sadly that didn’t happen with the home side running out 2-0 winners.
Clyde hit either side of the break to ensure East Fife returned to the kingdom empty handed, goals coming from Ally Love and Lewis Jamieson.
Boss Stevie Crawford refused to be too hard on his side, but conceded they failed to ask enough questions of their hosts.
He said: “We huffed and puffed our way through to half time and then in the second half I tried to get a bit more out of the boys.
“They’ve been great.
“For a few months we’ve been absolutely magic in terms of our commitment and effort.
“But I just felt the game wasn’t going our own way and Clyde put a foothold on the game.
“Other than the goals we’ve lost, we’ve no given right to come to Clyde and win games of football.
“In recent weeks when we have lost games I’ve been very praiseful of the team because we’ve created chances but, against Clyde, we never caused enough problems in the final third of the park.”
Danny Denholm was unlucky not to open the scoring with just a couple of minutes on the clock as East Fife made a positive start to the game.
Aaron Splaine had Clyde’s best opportunity but saw his effort blocked by Fife goalkeeper Jude Smith.
East Fife went behind when Ally Love managed to sneak his finish over the line.
Denholm again went close for East Fife as they tried to haul themselves level but it was Clyde who grabbed the game’s crucial second goal when Lewis Jamieson broke clear of the Fife defence and beat Smith.
Aaron Steele, Mikey Cunningham and Denholm again all had chances to get on the scoresheet but nobody could find the back of the Clyde net.