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The Giallorossi took the lead after less than a minute but were then forced to play the final 40 minutes with 10-men, in an erratic game at the Stadio Bentegodi that ultimately ended in a 1-0 win.
Cengiz Under got Roma's only goal of the game, as the side ended a run of six league games without a win.
"It was a very difficult match," Strootman said. "We could have killed it off in the first half with three great chances, but it stayed 1-0 and that's always dangerous.
"We fought hard when we went down to ten men: we weren't playing anymore but thankfully we didn't concede. Now we'll work hard ahead of the next game."
Despite the win, the midfielder was asked about the side's inability to get a second goal.
"But [at least] we scored. Against Sampdoria [last week], we had a couple of big chances early on and couldn't convert them," Strootman said.
"We had more luck today and we could even have scored more - including myself with that amazing last chance - but ultimately the main thing is that we take home the win."
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