I'm not a phonetician, but my understanding is that pretty much no language has physical "gaps" in the sense of actual periods of silence between subsequent words. (I think that this would be pretty inefficient from the point of view of communicating the greatest amount of information in the shortest amount of time.) So the idea of "gaps" is probably an abstract way of describing some feature of English pronunciation that is realized in some other way.
Different languages may "mark" word boundaries in different ways. One important part of this is intonation, which is I think a pretty difficult part of learning a different language. This can include things like modulation of pitch, volume, and duration of particular sounds (e.g. shortening some sounds, as in English "vowel reduction" in unstressed syllables, or lengthening some sounds).
The perception of "gaps" in English might be related to its word-final consonants
Aside from intonation, there are also various particular ways that word boundaries can be detected based on the rules about which sequences of sounds are allowed within a word in a particular language. For example, in English, no word ends with the sound /h/, and no word starts with the sound /ŋ/. There are various other rules in English about which sounds can occur where. One reason why these may create a greater sense of "gaps" in English than in certain other languages is that English has many different consonants and consonant clusters that can occur word-finally. For example, in a phrase like "take down", there is a "kd" sequence which is not possible word-initially or word-finally, and rarely found word-medially (I think only in compounds and a few infrequent prefixed Greek words like anecdote); some listeners might perceive a "gap" between these two consonants even if the phrase is not actually pronounced with a literal gap between the "k" of the first word and the "d" of the second.
In Spanish, words that do not end in a vowel usually end in one of a fairly restricted set of consonants: s, n, r, l, and rarely others such as θ, d or x. Consonant clusters starting with s, n, r, or l also occur in internal positions in Spanish words (although I'm not sure that all possible combinations that can arise between words exist).
I haven't studied or been exposed to Telugu at all, but Wikipedia tells me that it is also a language with a very restricted set of possible word-final consonants:
Telugu words generally end in vowels. In Old Telugu, this was absolute; in the modern language m, n, y, w may end a word.
And on the other hand, I know that German, another language that is often impressionistically described as having "gaps" between words, has many words that end in various consonants or consonant clusters.
To avoid sounding like you are pronouncing Spanish with "gaps", pay attention to the processes of consonant allophony and synalepha of vowels across word boundaries
In Spanish, the sound of a consonant at the start of a word may be affected by the final sound of the preceding word, if both words are in the same "intonational phrase". The "voiced" sounds represented by the letters b/v, d and g tend to be realized as approximants (or perhaps weakly articulated fricatives) after vowels, and as plosives after a preceding nasal consonant. (After liquids, the situation is a bit more complicated: it seems that typically /d/ alone is realized as a plosive after /l/, while /b/ and /g/ are realized as approximants in this position, and all three sounds are realized as approximants after r.) See guifa's answer to the Spanish SE question How should I pronounce the Spanish consonant 'd' for some concrete examples.
Another aspect of Spanish pronunciation that involves word boundaries is "synalepha": pronouncing two vowels in one syllable. This is usual for adjacent vowels in separate words.
To avoid sounding like you are pronouncing Telugu with "gaps", perhaps study intonation
Unfortunately, since I am not familiar with Telugu at all, I don't know of any particular steps that you can take to avoid sounding like you are putting "gaps" between words. However, one thing I see in Wikipedia's description of Telugu that seems like it might be alien to an English speaker is that the language is said to have no contrastive stress, and not even any particularly clear rules about where stress ought to fall in a word based on just the sounds contained in the word. French (a language that I know more about) is likewise a language without contrastive stress, and I think it can be difficult for English speakers to understand how to acquire correct intonation for a language like this.
I would recommend paying careful attention to how Telugu speakers pronounce phrases, and to avoid as much as you can any "English habits" that you are perhaps inadvertently bringing into your pronunciation such as thinking of words as having one syllable that must be strongly stressed in all contexts.