His team take on city rivals Hearts tomorrow, but Stubbs' attention yesterday was turned instead to the perception that the Tynecastle side's relegation has been "forgotten".
Both Edinburgh clubs went down to the SPFL Championship following similarly uncomfortable campaigns, although Stubbs has been given to feel that only his side carry the stigma of relegation. It perhaps rankles all the more given the scale of rebuilding being undertaken by Hibs.
The Easter Road side dropped out of the top flight following defeat in the play-off final against Hamilton Academical, a result which Stubbs suggested continues to mark his club.
"I think a few people forget that Hearts went down as well. It's not just Hibs that went down, it was Hearts that went down," said the Hibs head coach, whose side opened the league campaign last weekend with a win against Livingston. "Sometimes I get the impression it's just one team that went down last season. It's just the general consensus from speaking to people that there is a cloud hanging over us.
"We're trying to move on from what happened last season. People talk about what happened having a negative effect on the players but it's the same for Hearts because their players need picking up. They went down as well, that's what I'm trying to allude to.
"For me the negative is outside, there is nothing in the dressing room, but you can use it as motivation for the players. If you look at everyone's perception, it's Rangers top, Hearts second and Hibs third. If they see it going that way, that's fine. We're quite happy to sit under the radar and quietly do our own thing.
"We're going there to try and cause an upset and change what's happened over the last couple of seasons that they've been the team that's gotten the results."
Stubbs is aware, however, that it is not simply bragging rights which are at stake for Hibs tomorrow. The two clubs are expected to compete for promotion this season, alongside Rangers.
"In the broad light it's a normal game but in the fan's eye it's not," added the Englishman. "It's big from a supporter's point of view and we'll have 3000 fans that want to come away from the game with a positive result. I'm not going to go there and put 10 men behind the ball."