The Irishman has come in for flak from supporters following a nightmare start to the season that saw them kick off the campaign with four straight defeats.
The Leith outfit were humiliated 9-0 on aggregate by Malmo in the Europa League qualifiers before suffering another mortifying defeat to administration-hit Hearts in the Edinburgh derby.
But Petrie issued a statement on Wednesday offering Fenlon a vote of confidence and it had the desired effect as the team bounced back from a goal down at Rugby Park to register their first win of the new term.
Craig struck both goals in the 2-1 win over Kilmarnock and insisted the Hibs players are fully behind their manager.
He said: "Obviously the players want him to stay. He has brought a lot of us to the club. There have been a lot of changes this season and it was going to take time for us to gel.
"But it is important that when we are not getting results we stick together. We've done that and got a result at Rugby Park. However, there is still work to do but we know we have players capable of getting results in the Scottish Premiership."
Craig cancelled out Barry Nicholson's stunning 25-yard volley which opened the scoring for Killie after 22 minutes when he headed home from Rowan Vine's cross 90 seconds into the second half.
He then outmuscled Darren Barr before lobbing Killie keeper Craig Samson 10 minutes from time to secure three precious points.
"It was great to get the winner, especially for the fans, because it has been a tough start," said the former St Johnstone player. "From the point of view of getting the first win of the season, I suppose there is a bit of relief there.
"A lot of people have had a lot to say and rightly so for some of them.
"It was up to the players to respond and we have done that. We never got carried away when the results weren't there. The manager has come out and backed us as players because the training has been good.
"There was a lot of panic outside and people saying things, but inside the club we just went about our business the same way and that will continue this week now that we have won.
"We need to get the fans back onside now but I feel we are going in the right direction."
While Hibs have now collected their first victory, Kilmarnock's wait goes on.
Having lost to Aberdeen on the opening day of the season before being frustrated with stalemates against St Johnstone and then St Mirren, the Ayrshire side are struggling to find their feet under new boss Allan Johnston.
The former Queen of the South boss was only appointed on June 24 and has struggled to make the necessary changes to his squad.
But midfielder James Fowler claims the players already at the club must take more responsibility.
He said: "Getting players in as early as you can always helps. It gets them in the group and allows the manager to get a good look at them and what they can do.
"We weren't able to really do that this summer but it's not an excuse. The manager wants to bring in another one or two because we have lost a lot over the last six to eight months that played regularly.
"So we do need to strengthen the squad again and it will take those who do come in time to settle. But the guys here have to do better as well."