"I'm more than pleased with the performance," Lennon said after goals from Diomansy Kamara and Robbie Keane had given his team the three points which ensured they will finish the season as SPL runners-up.
"I saw a team out there today, working for each other, hunting in packs. And some of the football was magnificent. I thought we were different class; professional, gritty when we needed to be. We've got a squad who are galvanising themselves and working for each other."
Although the Scottish Cup semi-final defeat by Ross County remains an indelible blot on his record since he took over from Tony Mowbray, Lennon seems confident he has a squad which can be more competitive. He would not turn down any offer of transfer funds from his board of directors, but he has at least received the kind of response from his players to suggest a wholesale clear-out is unnecessary.
Asked if he thought the club should have made a better fist of their challenge this season, he replied, unsurprisingly, with a resounding yes. "I think so, yeah. We should have done with the quality and the players that we've got in the squad. But the players know that. They know they haven't done themselves justice."
Celtic had to work hard for their win in what became a bad-tempered contest, and Lennon admitted he had hoped for firmer officiating. "I thought the referee should have stamped down on it a lot earlier. For me there was only one team trying to win the game. I thought they were a wee bit crude in some of the challenges at times.
"I've got to give credit to my boys. They stood up to it. I think Scott Brown looked like he was enjoying himself out there, enjoying the physical battle. It looks like he's back near enough to his best. We asked them to stand up to it. We worked on a few things Dundee United have done over the last few weeks on the DVD last night. We just said don't be bullied. There was a wee stramash today and they were all over in there. I don't mind that. I don't want them to be intimidated any more."
Lennon agreed this Celtic side now appear to have taken on something of his own character, such as the willingness to persevere for as long as it takes to get results. "Probably, yeah. Going away from home, earning the right to play football. I like the balance between a bit of dig and entertainment value," he said.
"I don't care if we have to do seven Champions League qualifiers. I don't know how many we're going to have to play next year. It was important to finish second, to end Dundee United's run. We've got some big games to look forward to. I think the players are whetting their appetite now."
Lennon seems to be whetting his own appetite for taking on the manager's job longer-term, but he refused to speculate on when he might expect a talk about his future. "I don't know," he said. "All I can do is thank the players today for their efforts. It was a wonderful result and performance, and it gives me something to think about."