The Gunners took the lead after a header by Emmanuel Adebayor, but Jeremie Aliadiere scored the equaliser for Boro.
“We have to be happy with a point,” Southgate told Sky Sports.
“We’ve played really well with a patched together back four and they were fantastic, the four of them. Their contribution was outstanding.
“We created some good chances, Stewart Downing had a really good chance and I’m really pleased, the lads have given everything and it was a really good point for us.”
