Former Celtic manager Lennon has been in charge of Bolton since October 2014 when he succeeded Dougie Freedman, who was appointed the Nottingham Forest boss earlier this month.
When the Northern Irishman came in at the Macron Stadium, the Trotters were at the foot of the Championship table with one win in 11 league games.
Bolton have now climbed up to 14th in the standings with 34 points from 28 matches, seven points above the relegation zone.
The former Premier League outfit also reached the fourth round of the FA Cup, narrowly losing 2-1 to Liverpool at home in the replay on Wednesday.
Next up for Bolton is a clash against Derby at the iPro Stadium in the Championship on Saturday, and McClaren knows the challenge his side will face in the match as well as for the rest of the season.
"The past month's results has been a collective effort,” he told reporters on Thursday, according to Derby’s official Twitter account. “We have a focus to get clean sheets and be strong at the back.
"It has been a good month on the whole, we have got great contacts with other clubs and we have been able to utilise that. We need to continue how we have been going, but we need to keep our feet on the ground. There is a long, long way to go.
"We are at the business end of the season and we know there is a job to be done individually and collectively. Bolton should have beaten Liverpool last night. I have great respect for Neil Lennon, he has done a great job.
"It is the start of a big month and we are going to need the squad. A lot of the work has been done and now we need to deliver."
Derby are currently second in the Championship table with 54 points from 28 matches, level on points with Bournemouth, who are ahead on goal difference.
The Rams will be favourites to win on Saturday, but Bolton could well take a point.