The former Middlesbrough boss saw his side go top of Group B with a 3-0 win, though they were made to work hard by their inexperienced opponents in southern France
Despite being frustrated by their inexperienced opponents for much of the match, goals from Jordan Obita, Jake Forster-Caskey and Jordan Cousins proved enough to take the Three Lions to the top of Group B.
Despite not putting the Middle Eastern outfit to the sword as many expected they would, Southgate was pleased with the way his side didn't get frustrated with their lack of opportunities in front of goal.
"It's a familiar challenge for us as we've had that in our qualifying campaign for the Under-21s," he told BT Sport.
"Tonight it was a little more difficult because the pitch was dry and bobby, so we weren't able to move the ball as quickly as we have done in the past.
"We scored some very good goals, we showed some patience and we kept our concentration defensively. There's little more we can ask of the players.
"It's a game we expected to win. Qatar were a little bit younger than us and with it being their first game they had that enthusiasm and desire to keep us out.
"It was about finding a way through and I thought in midfield we were composed enough to keep probing, albeit it's taken two very good strikes to get us off the mark."
England now face reigning champions Brazil on Monday, and Southampton's James Ward-Prowse, who captained the side in the absence of Jack Butland, believes England will have to be at the top of their game to beat the holders as well as South Korea and Colombia in their remaining group games.
"We watched a lot of videos of Qatar and they caused us a lot of problems defensively. We knew they were going to be difficult to break down," he told BT Sport.
"We knew we had to be patient and keep probing away. It took a great strike from Jordan to open the scoring.
"They're [other group opponents] obviously good teams with very, very good players. We've just got to go through our recovery and go again on Monday."