Agnew's side are six points adrift of safety having failed to win in the league for nearly four months, while they have scored just 22 goals - two fewer than Everton's Romelu Lukaku.
At full time the Chilean, whose future in north London is extremely murky, made his way over to the travelling supporters who had made the 250-mile trip to the North East.
They still face crucial league games away at Tottenham and at home to Manchester United where they can not afford to drop any points.
Boro matched their more-fancied opponents until Mesut Ozil score the victor in the 71-minute, after Alvaro Negredo had cancelled out Alexis Sanchez's sublime opener.
After the win, Sanchez delighted the fans with his gesture.
Ramsey was also asked about the 3-4-3 formation Wenger deployed: "We've been working on our formation all week and I think it worked tonight".
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The Englishman is now a cornerstone in Middlesbrough's side, and has been one of very few performers for Boro in a season to forget.
Antonio Conte's side slipped to a 2-0 defeat to Manchester United on weekend and Spurs' form has seen them move just four points behind them.
Middlesbrough are in grave danger of being relegated to the Championship yet have one of the best defensive records in the league, conceding only 37 goals.
Middlesbrough may be without a League win since the middle of December, but they have been securing many home draws and are desperate to finally get a win under their belts as they try to claw their way out of the relegation zone.
"It's going to be tough, we know that", he said.
Despite the result, Arsenal's chance of finishing in the top four remain slim. "We need to get a win as soon as possible and change the face of it".