The Eredivisie outfit recorded a 2-1 away win on Thursday and the Eindhoven club's head coach had nothing but praise for their performance
Goals from Tim Matavz and Ola Toivonen gave PSV an early 2-0 lead before the Turkish side pegged one back and Rutten praised his team for the way in which they held on to their lead.
"We controlled the game pretty much for the 90 minutes, although we conceded a goal," he said during the post-match press conference.
"It could have been a different match, though, if Andreas Isaksson had not pulled off a first-minute save to keep us in the game. All in all, the team put in a mature performance.
"I had a gut feeling we could win here tonight. We had watched several of Trabzonspor's games. At first I thought we were in for a tough night with the home crowd cheering their team on, but we put in a mature performance.
"It is hard to dominate a game from start to finish also because Trabzonspor improved after the break. We have earned a vital away win and have a good chance of progressing to the next round. We must be wary of complacency, though: there is still the return leg in Eindhoven."
The second leg takes place at the Philips Stadium on February 23.