Spurs blew a 2-0 lead to concede twice in the final ten minutes before losing the penalty shootout 4-3.
Afterwards, former Spurs winger Lennon said: "You can see that the Tottenham players are hurting. As a player you know games you should win and this was one of them.
"Five minutes to go, 2-0 up, see it out. Even when it goes to 2-1, you've got to know how to see a game out.
"Tottenham didn't handle that well enough.
"I still think Tottenham need a few players in. There are links with Eberechi Eze and Savinho. Losing James Maddison and Son Heung-min is huge for this football club - two big players and big characters and leaders, and lots of goals and assists."
Lot of good things from Spurs
Meanwhile, ex-Spurs midfielder Murphy also told BBC Sport: "Tottenham went man for man and gained control with their discipline. It has to be done perfectly and you can see they have worked on it.
"The good thing for Tottenham was even when they dropped deep they were OK. There were a lot of good things for Tottenham fans from that first half.
"Set-plays were a big part of Frank's Brentford last season and I think that will be a good thing for Tottenham this season.
"I think to get back into the European places and have a good run in the Champions League, that would be realistic. I think there is lots to look forward to: better competition for places, younger players with more experience and there are still a few weeks left in the window."