What is more, his manager, Bruce Rioch, encouraged him to do so after Hartson had made the most of Wright's current suspension with the goal which wrapped up Tuesday's 4-2 Premiership win against Sheffield Wednesday.
That victory left Arsenal third in the Premiership and Hartson hopes to stay in the side on Sunday against Blackburn - and make it difficult for Rioch to offer Wright an automatic return in next week's Coca-Cola fourth round, also against Wednesday.
"I give 100 per cent every game and if I score as well it will help keep me in the team. That's the target," said Hartson, whose pounds 2.5m transfer from Luton last January broke the British record for a teenage transfer.
Hartson went on to score eight goals in 21 appearances and became an important member of the side that reached the Cup-Winners' Cup final.
But his chances have been few and far between since the summer arrival of Rioch and pounds 7.5m Dutchman Bergkamp from Internazionale.
"The start of this season was frustrating because I wasn't in the team," Hartson admitted. "Dennis got off to a slow start but he is buzzing now and Wrighty is always going to score goals, so you can't really blame the manager for keeping the same front line."
He added: "The competition for places keeps you on your toes and it's just great to be training in the same company as people like Wrighty, Dennis and Paul Merson.
"But every player in football is disappointed when they are not in the side and it's nice now for me to get a chance."
Meanwhile, he recognised how Bergkamp's presence is rubbing off on the rest of the squad, something which can have long-term benefits on Hartson, his club and his country.
"My international career has dipped a bit because I haven't been in the Arsenal first team scoring goals," he said.
"I'm only 20 and have got a lot of learning to do, and in that respect Dennis has been a big help.
"He stays out quite a lot on his own training and he talks a lot. . . encourages you all the time. He's got a great attitude."
Hartson is not the only one who has suffered through the competition, something underlined by the second half arrival of Paul Dickov against Wednesday.
Like Hartson, Scotland Under-21 striker Dickov hit his first goal of the season and he, too, will be hoping for further involvement this weekend against Alan Shearer and company.
The other part of north London is happy because Chris Armstrong is overcoming a difficult beginning to his Tottenham career to emerge as a quality replacement for Jurgen Klinsmann.
The 24-year-old striker was labelled a flop earlier this season after making a pounds 4.5m move across London from Crystal Palace to White Hart Lane but after a slow start he is now on a hot streak, and Tuesday's goal which clinched a 1-0 win at Middlesbrough - moving Tottenham to fifth in the Premiership - was his fifth in six games.
"Chris had a lot of pressure when he first joined us because he was taking over from Jurgen," Gerry Francis, the Spurs manager, conceded.
"He didn't score straight away but he was making a lot of goals for Teddy Sheringham - and I couldn't care less who scores the goals as long as someone does."
More importantly than his goal tally, Armstrong has plugged the gaps made by the close-season departures of Klinsmann to Bayern Munich and Nicky Barmby to Middlesbrough to forge a productive partnership with Sheringham.
"They've scored 20 between them and I was told the other day that that's more than Teddy and Jurgen had got together at the same stage of last season," Francis said.
"Chris has now got seven and Teddy's got 13, which is good. But my priority is for my players to play well - sometimes a striker can score a goal in a match but not play particularly well."