The U’s twice scored late equalisers to snatch a 3-3 draw at Accrington Stanley in their FA Cup second round clash.
Yesterday’s third round draw then handed the winners of the replay – which will be on Wednesday, December 12 – a home tie with Sheffield United in the third round.
Saturday’s match, however, was overshadowed by the death of Cole, who was just 27.
Nearly half of Saturday’s squad played alongside the U’s winger before he was forced to retire last year due to a heart condition.
They learned of his death just hours before kick-off.
Constable, one of United’s goalscorers, was a player who knew Cole well, and the striker admitted it had been tough.
He said: “It’s just devastating that this happened to such a young lad, obviously the thoughts are with his family and friends.
“I knew Mitch well. He would have wanted us to go out there and try to get a result. “I think the lads were affected after finding out and we were desperate to try and get a result.”
An emotional U’s manager Chris Wilder paid tribute to the way his side had applied themselves in the circumstances.
“We had a meeting just before we set off from the hotel and said as professional footballers we have an obligation to go out there and give it our best and I think you saw that we did that,” he said.
“I’m proud to be the manager because they’ve got off the canvas so many times.”
Progressing into the third round would give the U’s a chance to make up for last season’s first round defeat at Sheffield United, when they lost 3-0 at Brammal Lane.
Assistant manager Mickey Lewis relished the possibility of meeting the npower League One side – the club that Wilder led to promotion as captain – but stressed no-one is thinking too far ahead.
He said: “It’s a really good draw, but there’s a lot of work to do and I’m sure Accrington will be saying the same.
“When we played them last year we didn’t do ourselves justice, so it’s an opportunity, if we go through, to produce a better performance.”