Tully told BBC Devon: "We've always said we want to look upwards rather than downwards.
"If we come to the situation where with four or five games of the season to go we're in with a shout, then we've got a hell of a chance."
Tuesday's 2-2 draw with Carlisle stretched Exeter's unbeaten run to three games, following wins over Charlton and Notts County.
"We've had a tough run in of games and to take seven points out of nine we've got to be delighted," added Tully.
"We've got to look forward now. We've got two homes games coming up and if we can capitalise on them it puts us right up in the play-off picture.
"We've shown that we're good enough and deservedly need to be higher up in the table."
Source: BBC Sport
Source: BBC Sport