He said: "Weston thoroughly deserved the win. We were poor from start to finish. Some of the players let themselves down on Saturday night by being unprofessional.
"They had no energy to run about. We are at a good standard and you can't do it.
"They let themselves down, other players down, but more importantly they let the fans and chairman down and I am absolutely livid. We got exactly what we deserved."
Despite the defeat, City are still fourth in the table, two points clear of Hemel Hempstead Town, who came from 2-0 down to draw 2-2 at home to St Albans City, but have played three more games than City.
And tonight's defeat makes Saturday's visit of third placed Maidstone United even more important and Tully will be looking for a big reaction from his squad.
They will certainly have to play far better than they did against Weston, who could easily have been out of sight at half time.
The visitors went ahead in the sixth minute when Scott Wilson was put clear down the left and he calmly lobbed Martin Rice to make it 1-0.
And if it was not for Rice and plenty of good fortune the match could have been over as a contest by half time after a lethargic City performance against the pacy Somerset side who offered a real threat every time they got forward
City''s best chance fell to Cody Cooke from Matty Jay's lay off but he blasted well over as they went in fortunate to be still in the match.
There was little improvement after the break with Rice again kept busy and City rarely looking capable of drawing level.
And it came as no real surprise when the visitors went 2-0 up after 76 minutes when City skipper Arran Pugh, in his last game before starting a two match ban, turned a Joe McClennan cross from the right into his own net,
Jay did give City a glimmer of hope with seven minutes left when his header from Ryan Brett's left wing cross went in off the underside of the bar, but in stoppage time Weston broke clear with substitute Jake Mawford deservedly making it 3-1 to end a chastening night for the home side.
CITY: Rice; Dawson, Pugh (capt) (Ash 76), Richards, Brett; Knowles, Cooke, Green, Jay, Vassell (Afful 54), Wright (Duff 54). Subs (not used): Adelsbury, White.
Yellow cards: Cooke, Vassell, Knowles.
WESTON SUPER MARE: Purnell; Simpson, Fortune, Keary, Llewellyn, Cane, McClennan (Wring 85), Plummer (Pope 74), Wilson (Mawford 74), Grubb (capt), Edge
Yellow card: McClennan.
Goals: Wilson (6) 0-1, Pugh (76 og) 0-2, Jay (83) 1-2, Mawford (0+1) 1-3.
Referee: Tim Wood.
Read more: http://www.westbriton.co.uk/Truro-City-v-Weston-super-Mare-match-report/story-29098102-detail/story.html#ixzz45h8eVKAX