The result ended a run of nine straight home defeats in the Barclays Premier League and ensured they avoided an unwanted place in the record books.
Another loss would have equalled the Premier League marks for longest home losing run and most home defeats in a season (14), which are both held by Sunderland.
Wolves had to ride their luck in a game largely dominated by Everton, who twice had the ball in the net but saw Nikica Jelavic and Denis Stracqualursi both denied by the offside flag.
Connor, whose tenure as interim boss ends with next week's trip to Wigan, said: "Everton have not lost in seven, they've scored four goals in three of their last four games, they're a team bang in form, so to get a clean sheet from our point of view is a good effort.
"It was important to try to leave the fans with something. If we couldn't win it then we wanted to take something from the game so they had something positive to go home with for the summer, and come back next year to support the club in its quest to be back in the Premier League.
"We tried to stay with the game, not concede goals, and nick something if we could. We took a point today [Sunday] and if we can go to Wigan and do the same then that's three games without defeat. That would stand us in good stead for next year."
The draw kept Everton a point above Fulham in the race for seventh place, with Liverpool a further three points behind but with a game in hand.
The Toffees had a good early chance when Tim Cahill shot straight at Dorus De Vries, and they were left with a feeling of injustice in the 28th minute when Jelavic was flagged offside as he fired passed the keeper, with replays showing the Croatian was level.
Wolves' best chance was a header from Christophe Berra over the bar, and the pattern continued after the break, with Marouane Fellaini and Jelavic particularly wasteful from good openings.
Jelavic thought he had made amends in the 73rd minute when his cross was turned in by Stracqualursi at the far post, but Fellaini, who had also lunged for the ball, was a yard offside.
Everton assistant manager Steve Round admitted his side had paid for a lack of composure in front of goal, saying: "The players are disappointed in the dressing room. We had enough dominance in possession and created enough opportunities definitely.
"We just couldn't take that defining moment, whether it was the pass or the final shot, and obviously we had a really good goal disallowed.
"I thought the second one was offside, Fellaini doesn't touch the ball but he does go for it, which makes him interfering. Recently we've been playing as well as that but taking the chances, and today [Sunday] we didn't."
Connor was again reluctant to discuss his own future after his winless record since taking over from Mick McCarthy in February stretched to 12 games.
He said: "I finish on May 13. I'll give the club a full review of the season and the club will decide what path to take and how they want to regain their Premier League status. I'll abide by whatever decision is made."