Despite failing to secure all 3 points, Arsenal moved back into sixth spot with 27 points from 17 games.
Wenger, who has reputation for keeping his powder dry in transfer, said there was no need for reinforcements.
Club officials blocked unhappy supporters from displaying banners calling for Wenger to be sacked.
Arsenal will also miss the services of Theo Walcott, who is still recovering from a thigh injury.
After a 3-0 defeat against Manchester City on Sunday, Southampton travel to Arsenal on Tuesday.
Welbeck powerful header in the 66th minute gave the Gunners the much needed three points.
Captain Mikel Arteta and striker Yaya Sanogo are the latest names on a growing injury list.
Arsenal beat Dortmund 2-0 to leave struggles behind, seal knockout passage in CL.
Meanwhile, leaving Slovenia with a 1-1 draw at Maribor gives Celtic the edge going into the second leg on Tuesday.
Ramsey suspended for 2nd leg after seeing red; Higuain salvage situation for Napoli.
Newly promoted side’s shock opening goal is shortlived after Blues step it up.
English season begins with a picture perfect start for FA Cup champions as they down EPL holders City 3-0.
Wenger admitted his side were not at full fitness for the traditional curtain-raiser to the season.
Wenger had delayed putting pen to paper on a new contract, despite stating publicly that he was planning to stay.
The Frenchman’s contract at the club expires in the close-season, but he has repeatedly assured both the club and their supporters that he would sign a new deal.