The Black Cats went down 4-2 to high-flying West Brom on Saturday, three weeks after losing 1-0 to Aston Villa at the Stadium of Light as they failed to build upon their 3-1 victory at Fulham last weekend.
There were boos from sections of what remained of a crowd of 36,390 on the final whistle and the club felt the need later in the evening to dismiss rumours that the Ulsterman had offered to resign.
However, O'Neill, who must now prepare his side for the visit of QPR and their new manager Harry Redknapp on Tuesday, has warned them not to bow to the pressure.
He said: "We have a lot of work to do, we accept that.
"What I don't want is players getting concerned and worried because we have lost the last couple of games here and suddenly everybody is against us."
The events at Craven Cottage proved to be something of a false dawn as the Black Cats found themselves 2-0 down by half-time against the Baggies, in part as a result of their own failings.
The visitors, who climbed into third place as a result of their win on Wearside, a fourth consecutive Premier League victory for the first time, went ahead on the half-hour in spectacular style.
Adam Johnson could only help on Gareth McAuley's long ball and Zoltan Gera turned smartly and set himself before smashing an unstoppable left-foot shot past the helpless Simon Mignolet.
The Belgium international has arguably been Sunderland's stand-out performer so far this season, but his afternoon took a turn for the worse two minutes before the break when he allowed Chris Brunt's overhit through-ball to slip from his grasp and Shane Long could hardly believe his luck as he walked the ball into an empty net.
Sunderland's response, which was not helped by the premature departures of both John O'Shea and Lee Cattermole through injury, gradually gathered pace, and they were back in it with 17 minutes remaining when substitute Craig Gardner's free-kick clipped fellow newcomer Marc-Antoine Fortune in the defensive wall and flew past keeper Boaz Myhill.
But West Brom looked to have wrapped it up eight minutes later when Johnson has harshly adjudged to have tripped Liam Ridgewell inside the box - replays showed there had been little, if any, contact - and substitute Romelu Lukaku thumped the penalty home with the minimum of fuss.
Stephane Sessegnon's close-range finish gave Sunderland late hope, but as the Black Cats surged forward in search of an equaliser, Fortune struck in the fifth minute of added time to round off a deserved victory.
O'Neill said: "I don't mind getting beaten four or five-nil if it means that we are trying to turn a deficit back around again.
"There was always that possibility that West Bromwich Albion would maybe get a third goal.
"As it turns out, Simon Mignolet made a really good save after we had got off to a good start in the second half, so that kept us going.
"But we have to show that fight and determination throughout the whole season, not for one, not for two games, three games.
"If we had got something out of this, that would have kept it going. As it turns out, it has knocked us back again, but we will go and we have got to be prepared for Tuesday now."
The Black Cats have now won just two of their last 20 league games, and their last three victories have all come against 10 men.
Baggies boss Steve Clarke was doing his best to keep feet firmly on the ground as he assessed a flying start to both the campaign and his managerial career.
But his club is reaping the rewards of steady development and astute investment with the likes of 25-year-old Argentinian midfielder Claudio Yacob having slipped seamlessly into the team he inherited.
Clarke said: "Claudio has come in from Argentina on a free transfer and he has been an outstanding signing for us.
"When I came to the Albion in the summer, I sat down with (sporting and technical director) Dan Ashworth and we spoke about what I wanted to do with the squad and what I could see as beneficial to the squad, and that was the type of midfield player I asked for.
"We were lucky to get him because he slipped under the radar a little bit. Dan had got a few scouting reports on him, I sat and watched six or seven dvds on him and decided he might do a half-decent job for us, and he has done more than that."