It is 50 years since Portsmouth beat Arsenal and yesterday that record appeared set to be smashed apart. A disjointed performance from Arsène Wenger’s team should have been exposed by a visiting side who, given their 4-1 home defeat by West Ham United on Boxing Day, were surprisingly sprightly and spirited. But a header from William Gallas in the 81st minute sealed their fate and plunged Tony Adams, the Portsmouth manager, into deeper trouble, having overseen only two victories since taking over from Harry Redknapp in October.

There were times in this encounter when Arsenal played as if wading through mud, but the truth, according to Wenger, is that his players have been “swimming against bad headlines”. It is difficult to imagine that the recent critiques of the club have had a tangible effect on the players’ ability to stick to their manager’s game plan, but Wenger clearly has had enough of the negative interpretation of the team’s performances this season and is intent on righting the wrongs he sees in the analysis of Arsenal’s form. As a consequence he overegged his praise a little.

“We were intelligent, mature, didn’t make mistakes and won the game against a side that defended very deep and very well and I believe in the end it was difficult to create chances, but still we had one or two chances that got us a win,” Wenger said.

“The team is maturing quickly and has shown great mental strength in the last six weeks. Since I have been here no team has got as much bad publicity and I don’t think it is fair because I want them to do well. They are showing great character and working extremely hard. It is maybe the team who needs the most support because it is the youngest I have had.

“We played at [Aston] Villa on Friday and you look at what came out after the game. It was like we had been disastrous, yet we got 2-2.”

Wenger is not a man to rush to the sales department, but he has acknowledged that if he does buy, he needs a player with experience. However, Gallas, his seasoned former captain, shrugged off the decision to strip him of that role for his public criticism of the team. A free kick from Denilson was whipped in from the left and Gallas bravely headed in past David James. The France defender is understood to want to leave the club, but Wenger said that he does not want to sell him and he praised the innate good timing of his runs into the box.

“I do not want to sell anybody and I think he [Gallas] answers everybody by the quality of his performances and that is what you want to do when you are a great player,” Wenger said. “He started as a striker and looks the most likely to score on set-pieces because he has the timing of the run.”

Portsmouth are three points above the drop zone and the transition from Redknapp’s tenure to that of Adams has not gone smoothly. Adams faces a tough new year as Portsmouth are more likely to sell than buy.

Adams opted to play Peter Crouch on his own up front and it nearly paid off when Marc Wilson’s cross from the left found the former Liverpool striker, whose header hit the post. A later free kick from Wilson, deputising for the injured Glen Johnson, also found the head of Crouch, but his effort was a soft one.

James was at his most infuriating and looked to have made a poor decision when Emmanuel Adebayor was put through. The Portsmouth goalkeeper came out and missed the ball, leaving Sol Campbell to challenge before Sylvain Distin cleared brilliantly as Adebayor stumbled.

Samir Nasri was Arsenal’s most effective attacking force and his corner was fumbled by James, but the resultant header from Mikaël Silvestre was blocked by Papa Bouba Diop, whose performance Adams described as “immense” and who later blocked a header by Nicklas Bendtner that should have been directed better.

Portsmouth passed adroitly and always seemed on the verge of a breakthrough. Nadir Belhadj wasted a good chance set up by the persistence of David Nugent and a backheel by Crouch. The home crowd became increasingly frustrated by the lack of chances and when Adebayor shot into side netting after James fumbled a cross by Denilson, it seemed the title race was over for them, but Gallas came to the rescue.

“We have first to reduce the gap before we speak about the championship,” Wenger said. “You could see again today, with the result of Chelsea at Fulham [2-2], that it is difficult for everybody and I believe everybody will drop points at the beginning of the year. The other three play against each other, so for us it’s about being consistent.”

None was as consistent as Adams in his time at Arsenal. “There’s only one Tony Adams” they sang at the end and indeed he is a rarity. Adams played only for Arsenal and was the club’s captain for 14½ years, which meant that he led Arsenal to league titles spanning three decades. He acknowledged the acclaim and although he looked downcast as he did so, few left the Emirates believing that his side had been outclassed.

Arsenal (4-4-2): M Almunia 6 B Sagna 5 W Gallas 7 M Silvestre 6 G Clichy 6 E Eboué 5 Denilson 5 A Diaby 5 S Nasri 7 N Bendtner 5 E Adebayor 5 Substitutes: C Vela 5 (for Eboué, 66min), A Ramsey (for Diaby, 75). Not used: L Fabianski, K Touré, R van Persie, J Wilshere, K Gibbs. Next: Bolton (h).

Portsmouth (4-1-4-1): D James 4 M Wilson 7 S Distin 6 S Campbell 6 N Belhadj 6 S Davis 6 D Nugent 5 P Bouba Diop 6 R Hughes 5 N Kranjcar 5 P Crouch 5 Substitutes: A Mvuemba 5 (for Hughes, 50), J Defoe (for Nugent, 88), N Pamarot (for Bouba Diop, 90). Not used: J Ashdown, H Hreidarsson, G Little, Kanu. Next: Man City (h).

Referee A Wiley Attendance 60,092