The Black Cats turned in one of their most enterprising displays of a difficult season to date on Wednesday night to push Chelsea all the way to the final whistle.
However, they ultimately came away on the wrong end of a 4-3 scoreline and empty-handed at the end of a night of mixed emotions at the Stadium of Light.
That left Gus Poyet's side rooted to the foot of the Barclays Premier League table and five points adrift of safety, but Dossena is confident the belief within the dressing room is strong enough to fuel a fightback.
He said: "We are frustrated because we scored three goals and came away with zero points. But this team has great character.
"Okay, we lost, but there is a long way until May and the other teams are not a long way in front of us.
"We have got another chance on Saturday to close the gap on the teams in front of us.
"We kept going [against Chelsea] night because the mentality here is perfect. The fans are behind us and we want to win for them.
"At the end of the day, we didn't get them any points, but the mentality here is strong."
Manager Poyet emerged from the dressing room to insist he is more confident than ever that Sunderland can turn their season around after seeing them initially take the game to the high-flying Blues, and then stubbornly refuse to allow them to run away with it as they turned the screw.
Jozy Altidore's first league goal for the Black Cats had given them a 14th-minute lead, but it was then that Eden Hazard took over.
It was he who crossed for Frank Lampard to level just three minutes later, and then fired the visitors ahead eight minutes before the break with a superb individual effort.
John O'Shea levelled five minutes into the second half, but an equally impressive finish by Hazard restored Chelsea's lead before Sunderland full-back Phil Bardsley managed to score at both ends within a minute at the death.
Both Jose Mourinho and Poyet saluted Hazard's brilliance after the game, and Dossena admitted it will be a relief not to have to face the Belgian again on Saturday, when Tottenham head for Wearside.
He said: "Hazard had a fantastic game and you don't come up against players like him or [Juan] Mata every week.
"We know Chelsea are a great team - I know Tottenham are good, but I don't think they're as good as Chelsea.
"We have to show the same heart and same character because it's a very important game."
The defeat was Sunderland's first on their own pitch under Poyet, but they were applauded from the pitch by fans who recognised both the effort and commitment which had gone into a performance which came up only just short, and further evidence of a recovery under the Uruguayan.
More of the same is exactly what will be required if they are to dent Tottenham's hopes of breaking into the top four this season.
Poyet knows what a big ask that will be with his players feeling both the physical and psychological effects of their showdown with Mourinho's men, but that is exactly what he will demand of them.
He said: "Now we need to make sure we recover because it was a massive effort. If you could see the players in the dressing room, they gave everything.
"But we don't have another team to go and play on Saturday, so we need to recover well and I need to pick the right team to beat Tottenham."