Stewart Downing’s second-half winner denied the Potters a Wembley appearance after former Reds striker Peter Crouch had cancelled out Luis Suarez's opener.
But Pulis could not fault the contribution from the travelling Stoke fans, who loudly backed their team throughout.
“I’m disappointed for them [the fans],” he told reporters.
“They have been the bedrock of what this club has achieved in the last five or six years that I have been here and I think it shows what we are like as a football club in respect to the community.
"We need them to get behind us now for the last six or seven home games of the season and we still need to get to 40 points."
The Welshman also felt his side failed to capitalise on a period of pressure following Crouch’s equaliser and was disappointed in the manner they conceded the eventual winner.
He added: “We were a bit unlucky not to go into half-time not winning the game. I think [Jonathon] Walters should have hit the target and I think we were playing well.
“Second half again we started slow and gave them a bit of a leg-up with a goal.
“It was a poor goal to concede losing possession in our own half of the pitch and when you do that against one of the top four or five teams in the country they punish you and that’s what the lad has done.”
Despite defeat, Pulis expressed pride at his side's achievements this season and underlined the progress they have made in the past few years.
“We have had a remarkable in season, with many things ground-breaking,” he added.
“It’s our third time in a FA Cup quarter-final on the bounce the club has never done that before and going into Europe and doing very, very well in Europe.
“We have done really, really well. We have just stumbled at the last hurdle and that has been a disappointment but you have to give credit for what the players have done so far.”