Jenkinson was handed a Premier League debut in Saturday's 2-0 defeat by Liverpool at the Emirates Stadium, which also saw 18-year-old centre-back Ignasi Miquel make his first top-flight appearance after Laurent Koscielny hobbled off with a back injury.
Given the current selection crisis facing Wenger - who will now be without midfielder Emmanuel Frimpong for the trip to Manchester United next weekend after the 19-year-old was sent off for two yellow cards - Jenkinson is confident he and his fellow youngsters can compete.
"Our squad is stretched - that is quite obvious - but the people who have come in have done well, so I don't think there can be too many complaints," Jenkinson, 19, told radio reporters.
"There are a lot of young players in the squad - me included. But we are there for a reason - people believe in us - and all of us young ones have to step up to the mark to take responsibility, and that is what we will do."
Jenkinson, who featured in the midweek Champions League play-off first-leg win over Udinese, added: "Everyone pulls together. There is a good group we have got here and everyone is united.
"We are going to have ups and downs, but that is part of football.
"We did well against Udinese and then things did not go our way with Liverpool.
"But we will bounce back. We have got a lot of quality and will come back from this, without a doubt."
Jenkinson was signed from Charlton in a £1million deal, and it has certainly been a meteoric rise for the defender, who had a spell on loan with non-league Eastbourne and Welling last season.
"If you look back a year ago, I would not have thought about this in my wildest dreams," said Jenkinson, whose family are all staunch Arsenal fans.
"Personally it is great to be involved and to be getting the chances to play.
"It is mixed emotions because of the result, but it is great having played my first Premier League game now and hopefully I can build on it."
Arsenal were certainly out of luck on Saturday, when Wenger was already without several first-team players because of suspension and injury.
The Gunners were reduced to 10 men for the final 20 minutes after Frimpong's rash challenge on Lucas Leiva, and went behind to Aaron Ramsey's own goal before last-minute strike from substitute Luis Suarez clinched victory for the visitors.
"It is very difficult to take that defeat on the chin with the effort we have put in," Wenger told BBC Sport.
Despite being expected to sign for Manchester City, amid rumours the £22million move had stalled, Samir Nasri produced a composed display - and was unfortunate not to see his darting run end with a goal in the first half when a 25-yard strike drifted just wide.
It remains to be seen if the France midfielder will be involved in the trip to Italy next week, having been suspended for the first leg.
Should he play, then Nasri would not be eligible for City in Europe were he to move.
Wenger said: "For us now the biggest problem is to lift the team and prepare for Wednesday night. If Samir can be with us, it is even better."
Asked if the midfielder would play, Wenger responded: "Why not?"