Their latest setback came with a 2-0 FA Cup quarter final defeat at Manchester United on Saturday, which saw Johan Djourou ruled out for the rest of the season with a dislocated shoulder.
It follows on from the disappointment of being knocked out of the Champions League round of 16 at Barcelona in midweek, after losing the League Cup final to Birmingham.
Now, with no trophies since they won the FA Cup in 2005, their only remaining chance of silverware is in the Premier League.
They currently trail Manchester United, who still have to travel to the Emirates, by three points but have a game in hand.
Wenger maintains that his players have the mentality to cope with the frustration and push United all the way in the race for the title.
He said: "I believe that we can do it but it's a good test for us now to show that we can regroup and show the mental strength and togetherness and respond quickly.
"We have a week without a midweek game for the first time in a long time. But we have a good opportunity to show that we are solid.
"I'm very disappointed that we lost three big challenges in a very strange way.
"One was in the last minute to a goal that came from nowhere, one was under strange circumstances in Barcelona and now this.
"We weren't outplayed but we were punished by a team that was more clinical than us."
Wenger was critical of the tackling of United's veteran midfielder Paul Scholes and admitted that his players had carried the disappointment of Barcelona into their trip to Old Trafford.
The Frenchman believes that still being in contention when United travel to Arsenal in May will be key to winning the title.
He added: "Things aren't going our way at the moment. We have to keep going and the players support each other and come back strong.
"It was a strange game, we put a lot in and at the moment the goalkeeper is always man of the match against us week in week out and we have to get over this period.
"Subconsciously the disappointment of Tuesday night has played a part in the game. You could see something has gone, not in our effort, not in our attitude but confidence-wise.
"I feel the pitch was good, the referee was good and the tackles of Paul Scholes were bad."
Sir Alex Ferguson was forced to field a team with seven defenders due to a host of injuries in his United squad.
But his team took the lead just before the half hour at Old Trafford through Fabio before Wayne Rooney added a second after half time.
Ferguson does not expect to have any players back for Tuesday's Champions League round of 16 second leg game against Marseille.
Michael Carrick and Darren Fletcher both missed the Arsenal game through injury, although Antonio Valencia returned after six months out with a broken ankle.
Ferguson said: "What we'll have is what you saw against Arsenal.
"There may be a slight chance Jonny Evans could be fit. Nani has made great progress but he hasn't trained yet.
"He's been on the bike and the stitches have done their bit. I could have him for Saturday against Bolton.
"I couldn't risk Scholes and (Ryan) Giggs because of Tuesday's game, it's such an important game for the club so with that in the mind and if you look at the injuries in midfield I had to come up with a plan or an idea to utilise our energy."
Edwin van der Sar was outstanding against Arsenal, prompting calls from supporters for him to reconsider retiring at the end of the season.
The Dutchman, 40, insists however he will not go back on his decision and Ferguson added: "He's a fantastic goalkeeper we just wish he was 21 rather than coming up 41 but nature catches you eventually in life."