The Black Cats hauled themselves out of the Barclays Premier League relegation zone and into the relative comfort of 15th place as a result of their 3-0 win over fellow strugglers Reading on Tuesday night.
Colback said: "We knew how important this game was and we have won it. There's a lot of relief. But that's not even half the job done."
With trips to Manchester United and Southampton, as well visits to the Stadium of Light by Manchester City and Tottenham, to come before the turn of the year, adding significantly to their 16-point tally could prove difficult.
"We know we are down there where we don't want to be and where we shouldn't be," Colback added. "And we need to start winning more games, especially here, and giving the fans something to cheer about."
The win was just Sunderland's third in 24 league fixtures dating back to last season, and their first against a side finishing with 11 men since March. However, club sources were at pains to point out privately beforehand that manager Martin O'Neill was under no pressure despite speculation to the contrary in some quarters.
And that was a message hammered home in person by owner and chairman Ellis Short in an impromptu and for-information-only briefing in the press room at the Stadium of Light before kick-off.
Asked about the mood in the dressing room after the final whistle, Colback said: "It's a lot better than it has been obviously. It's one of the best feelings you can get in football when you win a game and everyone is buzzing and the fans go home happy. It's certainly something that we want to keep on doing."
That may be a tall order this week at least with Sunderland facing the task of attempting to upset the odds at Old Trafford. However, Colback is confident they can run out with heads held high having proved to themselves that they can win football matches.
He said: "When you go to the top teams, people say you won't pick anything up, but we will certainly be going there looking to hurt them. We are a dangerous side to play - we showed that when we went to Everton. We probably should have come away from that game with a win, so we will certainly be going into it with belief that we can get something."