Liverpool manager Brendan Rodgers was pleased with the way his side battled back in the 2-1 defeat at Manchester United.
Robin van Persie gave United a first-half lead and Nemanja Vidic extended their dominance in fortuitous fashion from a free-kick early in the second half.
But substitute Daniel Sturridge's first league goal for Liverpool brought the visitors back into the game and there were one or two nervy moments for the hosts in the closing stages.
Rodgers said: "I was very proud of the team. I thought that the first half we were a wee bit tentative at times in our passing and we actually presented them with opportunities in the game
"But in the second half - you could have easily at 2-0 given up the fight - the fightback was brilliant by the players and I thought second half we maybe deserved something from the game.
"We are disappointed to lose but take heart from the fact we kept going and Daniel Sturridge coming on and getting another goal was terrific. The second-half performance was much better.
"It's never easy when you have got young players that are making their debuts at Old Trafford and when you look at Manchester United's experience in their team - they have been there and been around a lot of them.
"For us it was just about reinforcing a couple of details that we needed to be better at. We are disappointed with the free-kick because we never defended that well enough. But after that the reaction was terrific.
"We will take great hope from the second-half performance. We know the improvements we need to make if we are going to sustain a challenge at the top of the table.
"There was 21 points difference before this game but it wasn't 21 points in terms of quality, it was 21 points in terms of the depth of the squad. So if we are going to be able to compete we need depth in our club that is going to enable us to compete on a consistent basis."
Rodgers also paid tribute to Sturridge who entered the action at the start of the second half.
He said: "I thought he was a real threat when he came on. He is an outstanding young player who just needed an opportunity. He will score many goals for Liverpool I am sure."
The three points established a six-point gap between the Black Cats and the Premier League relegation zone despite O'Neill having to contend with a lengthy injury list.
But the fact that it was achieved without a single specialist full-back illustrated the club's need for reinforcements, and the process of strengthening the squad was continuing with Al Hilal defender Kader Mangane due on Wearside in an attempt to tie up a loan move.
Nevertheless, as O'Neill prepared to attempt to lure new recruits to the Stadium of Light, he did so with a fresh spring in his step.
He said: "We are trying our best, obviously, to try to bolster the squad, which will be very, very important if we can do.
"But again, the great thing about the win, which is I suppose reminiscent of last year, only for 24 hours or 48 hours it takes a little bit of pressure off. It gives you a bit of respite and gives you a chance to look again."
The Ulsterman makes no apologies for establishing as his primary target the retention of the club's top-flight status and as a result, he will continue to look anxiously over his shoulder until that is achieved.
However, a fourth victory in seven league games provided further evidence that they are moving in the right direction.
But it was the manner as much of the fact of it which gave the Black Cats so much cause for optimism.
Admittedly, the Hammers were a pale shadow of the side which very nearly dumped Manchester United out of the FA Cup last weekend, but Sunderland took full advantage to dispatch them with the minimum of fuss.
Adam Johnson and Steven Fletcher had both gone close before Sebastian Larsson blasted the home side into a 12th-minute lead with a superb strike.
Visiting keeper Jussi Jaaskelainen was repeatedly left unprotected by a defence which lacked both shape and resilience, and they self-destructed in horrific fashion two minutes after the restart as Sunderland doubled their lead.
Sessegnon and James McClean tore the Hammers apart in a lighting break and although Jaaskelainen denied the Republic of Ireland international with a fine save, full-back Dan Potts' attempt to chest the rebound back to his keeper was intercepted by Fletcher and Adam Johnson poked home the loose ball.
McClean completed the most comprehensive of victories with his side's third 16 minutes from time before debutant Alfred N'Diaye passed up a glorious opportunity to make it four with his first touch after being introduced as a late substitute.
O'Neill said with a smile: "I must admit, he is rather disappointed with himself - and I am disappointed with him as well.
"That would have been fantastic for him. But he is very competitive, he is full of energy and I honestly think he will do very well for us."
Twelve months ago, Sunderland put together a run of seven league wins in 10 attempts in the wake of their new manager's arrival to pull away from the drop zone, and O'Neill spotted signs of a similar potency returning to his team on Saturday.
He said: "I know this time last year, we won a couple of games, against Swansea and then we followed it up with Norwich - that was a great performance.
"But you have to score the goals to make sure that the performance stays with you."
