Now in sixth place, the Gunners trail fourth-place Manchester City by seven points, but the London club have a game in hand.
Arsenal beat relegation-embattled Boro 2-1 on Monday to keep alive their faint hopes of a top-four finish.
"Mathematically it is still possible, even if it is hard, but we will give it a go", Wenger said after the victory at the Riverside.
Wenger experimented with a back three of Gabriel, Laurent Koscielny and Rob Holding, and the 67-year-old explained that he had grown concerned about the Gunners' susceptibility to conceding from direct approach play.
Of the formation employed in the north east, the Frenchman said: "I just felt that sometimes the team needs to believe in something new, something different, just to find a bit of confidence back".
"We needed to play forward a little bit earlier, and I thought we did that, and when we scored the goal I thought we would start to put them under pressure".
He added: "It was a testing point for us mentally, of course that was a moment where I felt that now we would see where we go".
He added: "I feel we are in a position where we want to perform".
"There was a bit of nervousness in our dressing room before kick-off because we had not had a good run and that can happen - confidence in life goes away quickly and comes back slowly - but this result helps".
Lampard leads tributes to John Terry's Chelsea career
The likes of West Bromwich Albion and West Ham United have also been linked with a move for Terry. 'Chelsea has been our life for so many years and will continue to be in the future.
He confessed: "What we've done previously has not been good enough".
Asked if the reluctance of Sanchez and Özil to sign new contracts had affected Arsenal's form, Wenger gave a cryptic reply.
"It worked well in the first half, we didn't give any chances away and we were quite solid on set-pieces".
"Despite sometimes hard situations, or some situations that lack clarity, we still can perform". We were in a bad situation with a lot of defeats and tonight we needed to come back with our quality.
"We needed to head out as well as return to the basic principles and that's making sure our obligation amounts were right. We have to take responsibility for that and we've done that this week between ourselves", he said.
"It's a massive honour to play for a team like Arsenal". We were tested just after half-time when they came back to 1-1.
"This group doesn't know how to give in, they will never, ever stop", he said.
"I couldn't be any more proud of the players".
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