A 2-0 defeat at home to Manchester City has condemned the Midlands club to life in the Championship next season.
"It's a very difficult day, a raw day for me the staff, the players, everyone connected with the club and it will be a tough few days to come," said Connor.
"Over 38 games we've proved not good enough to stay in the Premier League.
"It's an honest league and we've signed up for 38 competitive games and the matches might have a bearing on other teams so we'll show honesty, integrity and try to win as many points as we can."
Wolves were promoted to the Premier League in 2009.