The Lions had battered the Barbarians and Western Force in their previous games but they had to dig deep following a ferocious start from the hosts.
Captain Warburton, playing in his first match of the tour, told Sky Sports 2: "It was great to get the win, it was a really tough one. We expected that all week. It was great for us - we knew the Reds in attack would offer a lot today and they made it tough for us."
Ben Youngs, who scored the Lions' only try of the game, echoed Warburton's sentiments, saying: "The boys worked very hard. Queensland brought it to us. The boys dug in.
"We knew we would be under pressure at times. We know we will get it right next time."
Lions coach Warren Gatland pointed to his side's character in the face of relentless pressure, while also feeling the tourists were hard done by with a couple of refereeing decisions.
Gatland added: "Pretty happy with that one. It was a tough game and the weather conditions didn't help. I thought we showed great character.
"They threw everything at us in the first 20 but we toughed it out. They just kept working hard.
"They keep digging for what was required. A couple of decisions didn't go our way but the boys stuck at it."
Reds captain Quade Cooper said: "The Lions are a great team - we are not happy about losing, but the effort we showed was great."
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