Striker Callum Paterson notched the only goal of a tight clash when he headed home in the second half, while Hibs had chances of theirown to score but were left licking their wounds over a fourth straight competitive defeat of the season.
The Leith side bowed out of the Europa League at the first hurdle following a 9-0 aggregate defeat, including an embarrassing 7-0 loss in the second leg at home, to Swedish side Malmo.
And following an opening day Premiership defeat against Motherwell, they have now been beaten in their first two league matches and a section of the Hibs supporters booed and vented their frustration at Fenlon at the final whistle on Sunday.
Thomson said: "The manager is quite happy to carry the can but, for me, it is down to the 11 boys he picks. We have to take a bit of responsibility.
"The manager is a good man and has brought in some good players. We could have been sitting here with a good start to the season but unfortunately we are not.
"The fans pay their money and are entitled to their opinion - some of them think I'm a good player and some think I'm rubbish.
"That's the industry we are in and some people will like the manager and some people won't. He is big enough and brave enough to take it on the chin.
"We will go in on Monday, work hard and try to get three points next week."
Asked if he hoped the club would stick by Fenlon, Thomson replied: "For the players, it does not involve us. Since I've been here, I think he is a good man and a good manager.
"The appointment of Jimmy Nicholl (as assistant manager) has been fantastic. He has been a breath of fresh air since he came in, but it's a results business and as players we have to stick together and get results.
"Hopefully the manager will see the rewards of bringing in some good football players."