Blackburn put in a good performance against the Gunners but failed to find an equaliser, with Marcus Babbel having a goal disallowed. However the boss was happy with his players' work.
"We've been here, to Stamford Bridge and to Old Trafford and shown we can play football with the best. If we keep playing like that we'll be fine this season." said Souness.
Souness wasn't without complaints though, and Pires was accused of going down to easily in tackles by the Rovers' boss after Vratislav Gresko, Andy Todd and Marcus Babbel were booked.
"Pires is a super player but he got two of our players booked and I felt that he goes to ground too easily."