City beat Tottenham 4-3 in Wednesday's quarter-final second leg at the Etihad Stadium, but it was not enough to stop them crashing out on away goals after a 4-4 aggregate draw following their 1-0 loss last week.
Guardiola therefore missed out on a reunion with Ten Hag, whose Ajax side produced another remarkable away performance to overcome Juventus in their last-eight tie.
The two managers worked together at Bayern, where Ten Hag coached the German giants' reserve team for two years before returning to his homeland with Utrecht and then Ajax.
City's conquerors Spurs now stand between the Dutch side and a place in the final of the Champions League, and Guardiola is wishing his former colleague well.
"I was lucky to meet him at Bayern and he was an assistant from the second team. We had a lot of chats," he said at Friday's news conference.
"I'm delighted where he is, a historical club. It would have been a pleasure to play him. I wish him a good two games and I will be watching on TV."
Ajax also knocked out three-in-a-row champions Real Madrid en route to the last four, and Guardiola is not ruling out a first continental success since 1995 for the Eredivisie club.
"They have more chances [to win the title] than Man City this season, so we'll see," he joked. "One stage more to go to the final."
Barcelona and Liverpool will contest the other Champions League semi-final after seeing off Manchester United and Porto respectively in the quarters.