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The Gunners were knocked out of both the FA Cup and Champions League this week.
Wenger's position has been questioned and his team's performances criticised but they won 2-0 at Goodison Park to stay third in the Premier League.
"I was pleased with how well they responded today," said Wenger.
"It was a very significant win for us and a mental test.
"I like this group, I like the mental attitude, it has been questioned and that hurts me," he added after Danny Welbeck and Alex Iwobi scored in the win over Everton.
"When you work with them every day, you see how much effort they put in."
Arsenal were top of the Premier League on 4 January and fighting for silverware in two cup competitions.
But their form has collapsed in recent weeks and Saturday's win was their first in four games in the Premier League.
They lost to Watford on Sunday in the FA Cup quarter-finals and a 3-1 defeat by Barcelona on Wednesday sealed their exit from Europe.
They are now 11 points behind leaders Leicester City and three behind second-placed Tottenham.
But Wenger does not think his side are out of the title race with eight games remaining.
"Why should it be a two-horse race with one team three points in front of us? Let's focus on performances and after that we will see how we finish," he added.

Welsh economy minister Edwina Hart said despite criticism of UK ministers, her counterparts in London know how important the industry is.
She met UK Business Secretary Sajid Javid on his visit to Port Talbot steelworks on Friday.
Tata Steel has said it would sell its UK business, putting thousands of jobs at risk.
Mr Javid said he had been concerned at talk of a time-frame for the sale of three to four weeks, but says there is now an understanding it is "much longer" than that.
Ms Hart told the BBC: "It's very important to recognise in UK terms we can't allow the steel industry to go.
"What happens to defence contracts, what happens now in terms of nuclear? We need a steel industry. I think the UK government is as aware of that as us.
"We've got to be hopeful, because it's important we keep steel, and that is what both governments are trying to do, to ensure we've got the best results in terms of the purchase of the plant."
Port Talbot has the largest steelworks in the UK, with 4,000 jobs at risk.
Tata has other Welsh plants at Trostre, Shotton, Llanwern and Newport, while UK plants in Rotherham and Corby are also affected.
Eluned Parrott, Liberal Democrat economy spokeswoman, said: "It is all very well for Sajid Javid to come here and promise action, but his words of support for the steel industry are in stark contrast to his record.
"The fact is that Mr Javid and his Tory colleagues have done nothing to mitigate this crisis."
Plaid Cymru leader Leanne Wood said: "Inaction and indifference by governments at both ends of the M4 mean that months of lost time have gone by in which decisive action could have been taken."
A UKIP Wales spokesman said Mr Javid arrives in Wales "with a long face but an empty portfolio".
"As long as we are members of the EU we cannot decide to change our tariffs on Chinese steel and we are condemned to paying artificially expanded rates for energy."
Britain Stronger In Europe, which is campaigning for the UK to stay in the EU, said the European Commission had a record 37 anti-dumping measures in place, with 16 of those specifically targeting Chinese imports.
Arsene Wenger said it "hurt" that his players' attitude was questioned and believes Arsenal passed a "mental test" to beat Everton on Saturday.
[NEXT_CONCEPT]
The UK and Welsh governments are working to keep steel production in Britain, a minister has said.